# Heavy vs. light flowers # Callin Switzer # 12 October 2016 # update 8 Dec 2017 # # Compares the bees' frequency when they are buzzing on # heavy (metal added) vs. light flowers # Note: all pores were glued shut
#install packages
ipak <- function(pkg){
new.pkg <- pkg[!(pkg %in% installed.packages()[, "Package"])]
if(length(new.pkg)) install.packages(new.pkg, dependencies = TRUE)
sapply(pkg, require, character.only = TRUE)
}
packages <- c("ggplot2", "reshape2", 'lme4', 'sjPlot', "multcomp", "plyr", "effects", "gamm4", "viridis",
"cowplot")
ipak(packages)## Loading required package: ggplot2## Loading required package: reshape2## Loading required package: lme4## Loading required package: Matrix## Loading required package: sjPlot## Warning in checkMatrixPackageVersion(): Package version inconsistency detected.
## TMB was built with Matrix version 1.2.10
## Current Matrix version is 1.2.11
## Please re-install 'TMB' from source or restore original 'Matrix' package## Install package "strengejacke" from GitHub (`devtools::install_github("strengejacke/strengejacke")`) to load all sj-packages at once!## Loading required package: multcomp## Loading required package: mvtnorm## Loading required package: survival## Loading required package: TH.data## Loading required package: MASS##
## Attaching package: 'TH.data'## The following object is masked from 'package:MASS':
##
## geyser## Loading required package: plyr## Loading required package: effects## Loading required package: carData## lattice theme set by effectsTheme()
## See ?effectsTheme for details.## Loading required package: gamm4## Loading required package: mgcv## Loading required package: nlme##
## Attaching package: 'nlme'## The following object is masked from 'package:lme4':
##
## lmList## This is mgcv 1.8-20. For overview type 'help("mgcv-package")'.## This is gamm4 0.2-5## Loading required package: viridis## Loading required package: viridisLite## Loading required package: cowplot##
## Attaching package: 'cowplot'## The following object is masked from 'package:sjPlot':
##
## plot_grid## The following object is masked from 'package:ggplot2':
##
## ggsave## ggplot2 reshape2 lme4 sjPlot multcomp plyr effects gamm4
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## viridis cowplot
## TRUE TRUE# set ggplot theme
theme_set(theme_classic() + theme(axis.text=element_text(colour="black")))
# define data and figure directories
dataDir <- "/Users/cswitzer/Dropbox/SonicationBehavior/SonBehData"
figDir <- "/Users/cswitzer/Dropbox/SonicationBehavior/SonBehFigs"
# print system info
print(paste("last run ", Sys.time()))## Warning in as.POSIXlt.POSIXct(x, tz): unknown timezone 'zone/tz/2017c.1.0/
## zoneinfo/America/Los_Angeles'## [1] "last run 2018-01-08 23:25:04"print(R.version)## _
## platform x86_64-apple-darwin15.6.0
## arch x86_64
## os darwin15.6.0
## system x86_64, darwin15.6.0
## status
## major 3
## minor 4.2
## year 2017
## month 09
## day 28
## svn rev 73368
## language R
## version.string R version 3.4.2 (2017-09-28)
## nickname Short SummerRead in data and do some visualizations
new_df = read.csv(file.path(dataDir, "02_HeavyLight_cleaned.csv"))
new_df$hive = as.factor(new_df$hive)
new_df$treatment <- mapvalues(new_df$treatment, from = c("sham", "weighted"), to = c("Sham", "Weighted"))
head(new_df)## freq amp datetime rewNum
## 1 250 0.17945 2016_09_28__09_59_13_112 1
## 2 300 0.56657 2016_09_28__09_59_14_520 2
## 3 400 0.68371 2016_09_28__09_59_15_030 3
## 4 410 0.80118 2016_09_28__09_59_15_707 4
## 5 370 0.52666 2016_09_28__09_59_16_277 5
## 6 360 0.31541 2016_09_28__09_59_17_096 6
## accFile beeID hive IT
## 1 2016_09_28__09_59_13_112_220_450_test.txt 7 3 3.98
## 2 2016_09_28__09_59_14_520_220_450_test.txt 7 3 3.98
## 3 2016_09_28__09_59_15_030_220_450_test.txt 7 3 3.98
## 4 2016_09_28__09_59_15_707_220_450_test.txt 7 3 3.98
## 5 2016_09_28__09_59_16_277_220_450_test.txt 7 3 3.98
## 6 2016_09_28__09_59_17_096_220_450_test.txt 7 3 3.98
## accFileAndFolder
## 1 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## 2 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## 3 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## 4 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## 5 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## 6 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## dateFrozenOrMarked treatment amp_acc
## 1 28-Sep-16 Sham 17.64503
## 2 28-Sep-16 Sham 55.70993
## 3 28-Sep-16 Sham 67.22812
## 4 28-Sep-16 Sham 78.77876
## 5 28-Sep-16 Sham 51.78564
## 6 28-Sep-16 Sham 31.01377# calculate average number of each treatment
ll = list(tapply(new_df$treatment, new_df$beeID, table))
dd = data.frame(unlist(ll))
dd$beeTrt = row.names(dd)
dd$beeID = sapply(dd$beeTrt, FUN = function(x) strsplit(x, "\\.")[[1]][1])
dd$trt = sapply(dd$beeTrt, FUN = function(x) strsplit(x, "\\.")[[1]][2])
# shows average number of buzzes per treatment
tapply(dd$unlist.ll., INDEX = dd$trt, mean)## Sham Weighted
## 29.69444 35.86111tapply(dd$unlist.ll., INDEX = dd$trt, sd) # sd for number of buzzes## Sham Weighted
## 9.603034 15.224328# show histograms of frequencies
hist(new_df$freq, breaks = seq(215, 455, by = 10))
# Calculate average for each bee and for each treatment
frqMeans <- as.data.frame(tapply(X = new_df$freq, INDEX = list(new_df$beeID, new_df$treatment), mean))
frqMeans$beeID <- row.names(frqMeans)
frqMeans## Sham Weighted beeID
## 1 344.3333 347.0833 1
## 10 331.2000 382.5000 10
## 11 411.7391 387.6923 11
## 12 344.8276 339.2500 12
## 14 324.0625 281.6000 14
## 15 367.5000 376.3158 15
## 16 357.0588 386.0606 16
## 17 314.0741 341.6000 17
## 18 366.4706 345.0000 18
## 19 375.0000 379.2308 19
## 2 298.5294 322.9167 2
## 20 359.8148 313.3333 20
## 21 331.3158 310.7143 21
## 22 399.4286 388.2857 22
## 23 348.2759 351.2821 23
## 24 287.7778 273.3333 24
## 25 345.0000 352.3684 25
## 26 369.6000 392.7273 26
## 27 366.6667 350.0000 27
## 28 364.4444 374.1935 28
## 29 291.2500 319.3333 29
## 3 399.0323 388.9655 3
## 30 368.0769 369.0323 30
## 31 273.5294 320.4167 31
## 32 325.6000 246.1538 32
## 4 356.6667 371.3636 4
## 5 370.7692 353.7143 5
## 6 284.2857 326.5714 6
## 7 366.9697 396.3415 7
## 8 333.8462 342.0833 8
## 9 344.4000 384.4444 9
## blue 319.1429 333.8462 blue
## gold 374.5098 365.2174 gold
## orange 309.6875 319.1000 orange
## pink 385.3333 367.5000 pink
## white 319.7674 326.9444 white# convert to long format for ggplot-ing
frqLong <- melt(frqMeans, id.vars = "beeID", measure.vars = c("Sham", "Weighted"),
variable.name = "trt", value.name = "frq")
nrow(frqLong)## [1] 72ggplot(frqLong, aes(x = trt, y = frq)) +
geom_boxplot() +
geom_line(aes(group = beeID))+
geom_point()
ggplot(frqLong, aes(x = trt, y = frq)) +
geom_boxplot() +
labs(y = "Buzz Frequency (Hz)", x = "Flower treatment")
#ggsave(file.path(figDir, "heavyLight_frq.pdf"), width = 5, height = 4)
# print some descriptive statistics
nrow(new_df)## [1] 2360unique(new_df$hive)## [1] 3 4
## Levels: 3 4# Calculate average amplitude for each bee and for each treatment
ampMeans <- as.data.frame(tapply(X = new_df$amp_acc, INDEX = list(new_df$beeID, new_df$treatment), mean))
ampMeans$beeID <- row.names(ampMeans)
ampMeans## Sham Weighted beeID
## 1 79.41488 49.082432 1
## 10 48.45538 30.837297 10
## 11 34.56381 22.888359 11
## 12 39.69695 36.219420 12
## 14 28.06241 22.151111 14
## 15 43.84567 39.297029 15
## 16 50.08044 36.654450 16
## 17 38.58280 34.215988 17
## 18 31.56744 23.471063 18
## 19 43.66984 24.653556 19
## 2 35.11669 34.075563 2
## 20 47.39991 35.394684 20
## 21 44.71363 34.498420 21
## 22 32.36932 24.702542 22
## 23 63.43800 46.047727 23
## 24 41.36935 22.975869 24
## 25 36.78398 20.052036 25
## 26 28.09219 22.162838 26
## 27 39.66976 30.902595 27
## 28 44.74322 39.945697 28
## 29 43.33800 22.381776 29
## 3 49.02683 56.246838 3
## 30 54.47406 29.037523 30
## 31 57.17575 30.517863 31
## 32 35.02128 5.009379 32
## 4 34.84784 37.962188 4
## 5 51.37301 32.967355 5
## 6 25.06068 36.736087 6
## 7 42.30789 47.528431 7
## 8 71.53457 28.270977 8
## 9 38.79524 29.125278 9
## blue 31.83149 19.595870 blue
## gold 34.72996 20.867171 gold
## orange 52.83226 46.007837 orange
## pink 30.62350 39.548159 pink
## white 22.55167 15.381023 whiteampLong <- melt(ampMeans, id.vars = "beeID", measure.vars = c("Sham", "Weighted"),
variable.name = "trt", value.name = "amp")
ggplot(ampLong, aes(x = trt, y = amp)) +
geom_boxplot() +
geom_point() +
labs(y = expression ("Sonication amplitude "(m~s^{-2})), x = "Flower treatment")
ggplot(ampLong, aes(x = trt, y = amp)) +
geom_boxplot() +
geom_point() +
geom_line(aes(group = beeID))
ggplot(ampLong, aes(x = trt, y = amp)) +
geom_boxplot() +
labs(y = expression ("Sonication amplitude "(m~s^{-2})), x = "Flower treatment")
#ggsave(file.path(figDir, 'heavyLightAmp.pdf'), width = 5, heigh = 4)
nrow(ampLong)## [1] 72Modeling frequency with GAMM
Use BIC to select model (decide what interactions and covariates to use)
Make sure that REML = FALSE when comparing BIC values
Start with the biggest model of interest, and then see what predictors can be removed
rr = new_df$treatment[1]
df1 = new_df[1, ]
for(ii in 1:(nrow(new_df) -1)){
if(rr == new_df$treatment[ii + 1]) next
else{
df1 = rbind(df1, new_df[ii+1, ])
rr = new_df$treatment[ii + 1]
}
}
df1 <- df1[df1$rewNum != 1, ]
df1$trtSwitch = df1$rewNum
colnames(df1)## [1] "freq" "amp" "datetime"
## [4] "rewNum" "accFile" "beeID"
## [7] "hive" "IT" "accFileAndFolder"
## [10] "dateFrozenOrMarked" "treatment" "amp_acc"
## [13] "trtSwitch"df2 <- df1[, c("beeID", "hive", "trtSwitch", "IT")]
df2## beeID hive trtSwitch IT
## 34 7 3 34 3.98
## 111 white 3 37 3.70
## 178 1 4 25 4.07
## 232 8 4 25 3.84
## 284 19 3 27 4.01
## 353 29 3 31 3.78
## 402 16 3 34 4.11
## 478 26 3 26 3.72
## 536 32 3 26 3.72
## 573 15 4 25 3.61
## 635 24 4 25 3.55
## 687 10 3 26 4.09
## 745 30 4 27 4.19
## 814 21 3 39 3.52
## 897 28 4 28 3.57
## 963 6 3 36 4.55
## 1002 orange 3 33 4.81
## 1129 17 4 28 4.25
## 1205 25 3 27 3.73
## 1267 31 3 25 3.76
## 1336 blue 3 36 3.91
## 1391 23 3 30 4.18
## 1459 12 3 30 4.10
## 1530 3 3 32 4.27
## 1594 22 4 36 3.65
## 1673 4 3 45 4.27
## 1710 9 3 26 4.17
## 1763 5 3 27 3.76
## 1832 2 4 35 4.42
## 1930 11 3 27 3.92
## 1986 20 3 34 4.28
## 2065 14 4 26 4.23
## 2127 pink 4 31 4.29
## 2204 27 3 34 3.51
## 2253 18 3 29 3.12
## 2310 gold 3 24 4.13sum(duplicated(df2$beeID))## [1] 0newdf2 <- merge(new_df, df2)
head(newdf2)## beeID hive IT freq amp datetime rewNum
## 1 1 4 4.07 310 0.65224 2016_09_27__10_52_32_696 1
## 2 1 4 4.07 330 0.47733 2016_09_27__10_52_41_293 2
## 3 1 4 4.07 240 0.55067 2016_09_27__10_52_42_247 3
## 4 1 4 4.07 290 0.28977 2016_09_27__10_52_42_974 4
## 5 1 4 4.07 360 0.47311 2016_09_27__10_52_51_809 5
## 6 1 4 4.07 360 0.45364 2016_09_27__10_53_00_124 6
## accFile
## 1 2016_09_27__10_52_32_696_220_450_test.txt
## 2 2016_09_27__10_52_41_293_220_450_test.txt
## 3 2016_09_27__10_52_42_247_220_450_test.txt
## 4 2016_09_27__10_52_42_974_220_450_test.txt
## 5 2016_09_27__10_52_51_809_220_450_test.txt
## 6 2016_09_27__10_53_00_124_220_450_test.txt
## accFileAndFolder
## 1 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 2 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 3 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 4 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 5 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 6 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## dateFrozenOrMarked treatment amp_acc trtSwitch
## 1 27-Sep-16 Weighted 64.13373 25
## 2 27-Sep-16 Weighted 46.93510 25
## 3 27-Sep-16 Weighted 54.14651 25
## 4 27-Sep-16 Weighted 28.49263 25
## 5 27-Sep-16 Weighted 46.52016 25
## 6 27-Sep-16 Weighted 44.60570 25newdf2$visitNum_centered <- newdf2$rewNum - newdf2$trtSwitch
# get treatment
trts <- (sapply(unique(newdf2$beeID), FUN = function(x){
startt = newdf2[newdf2$beeID == x & newdf2$rewNum == 1, "treatment" ]
return(as.character(startt))
}))
df4 <- data.frame(beeID = unique(newdf2$beeID), trts = trts)
newdf3 <- merge(newdf2, df4)
newdf3$trt2 <- as.factor(paste(newdf3$trts, "first"))
head(newdf3)## beeID hive IT freq amp datetime rewNum
## 1 1 4 4.07 310 0.65224 2016_09_27__10_52_32_696 1
## 2 1 4 4.07 330 0.47733 2016_09_27__10_52_41_293 2
## 3 1 4 4.07 240 0.55067 2016_09_27__10_52_42_247 3
## 4 1 4 4.07 290 0.28977 2016_09_27__10_52_42_974 4
## 5 1 4 4.07 360 0.47311 2016_09_27__10_52_51_809 5
## 6 1 4 4.07 360 0.45364 2016_09_27__10_53_00_124 6
## accFile
## 1 2016_09_27__10_52_32_696_220_450_test.txt
## 2 2016_09_27__10_52_41_293_220_450_test.txt
## 3 2016_09_27__10_52_42_247_220_450_test.txt
## 4 2016_09_27__10_52_42_974_220_450_test.txt
## 5 2016_09_27__10_52_51_809_220_450_test.txt
## 6 2016_09_27__10_53_00_124_220_450_test.txt
## accFileAndFolder
## 1 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 2 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 3 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 4 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 5 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 6 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## dateFrozenOrMarked treatment amp_acc trtSwitch visitNum_centered
## 1 27-Sep-16 Weighted 64.13373 25 -24
## 2 27-Sep-16 Weighted 46.93510 25 -23
## 3 27-Sep-16 Weighted 54.14651 25 -22
## 4 27-Sep-16 Weighted 28.49263 25 -21
## 5 27-Sep-16 Weighted 46.52016 25 -20
## 6 27-Sep-16 Weighted 44.60570 25 -19
## trts trt2
## 1 Weighted Weighted first
## 2 Weighted Weighted first
## 3 Weighted Weighted first
## 4 Weighted Weighted first
## 5 Weighted Weighted first
## 6 Weighted Weighted first# GAMM
# start with gamm so I can show change by visit number
g01 = gamm4(freq ~ s(visitNum_centered, by = trt2) + IT + hive + treatment + trt2, random = ~(1|beeID), data = newdf3)
par(mfrow = c(2,3))
aab <- plot(g01$gam, all.terms = TRUE, rug = FALSE, shade = TRUE)
summary(g01$gam) # Summary for paper ##
## Family: gaussian
## Link function: identity
##
## Formula:
## freq ~ s(visitNum_centered, by = trt2) + IT + hive + treatment +
## trt2
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 373.350 64.000 5.834 6.17e-09 ***
## IT -5.075 15.811 -0.321 0.748
## hive4 -4.208 11.433 -0.368 0.713
## treatmentWeighted 1.919 3.431 0.559 0.576
## trt2Weighted first -10.607 10.771 -0.985 0.325
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered):trt2Sham first 1 1 1.470 0.225
## s(visitNum_centered):trt2Weighted first 1 1 1.015 0.314
##
## R-sq.(adj) = -0.000401
## lmer.REML = 25097 Scale est. = 2354.9 n = 2360summary(g01$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 25096.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3193 -0.4698 0.1892 0.6934 2.3814
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 9.602e+02 3.099e+01
## Xr.0 s(visitNum_centered):trt2Weighted first 0.000e+00 0.000e+00
## Xr s(visitNum_centered):trt2Sham first 3.028e-11 5.503e-06
## Residual 2.355e+03 4.853e+01
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 373.350 64.000 5.834
## XIT -5.075 15.811 -0.321
## Xhive4 -4.208 11.433 -0.368
## XtreatmentWeighted 1.919 3.431 0.559
## Xtrt2Weighted first -10.607 10.771 -0.985
## Xs(visitNum_centered):trt2Sham firstFx1 2.285 1.885 1.212
## Xs(visitNum_centered):trt2Weighted firstFx1 2.569 2.550 1.007
##
## Correlation of Fixed Effects:
## X(Int) XIT Xhive4 XtrtmW Xtr2Wf X(N_):2Sf
## XIT -0.992
## Xhive4 -0.043 -0.011
## XtrtmntWght -0.041 0.011 0.003
## Xtrt2Wghtdf -0.237 0.165 -0.014 0.051
## X(N_):2SfF1 0.049 -0.028 -0.008 -0.707 -0.038
## X(N_):2WfF1 -0.032 0.012 -0.002 0.658 0.063 -0.466dev.off()## null device
## 1g02 = gamm4(freq ~ s(visitNum_centered, by = trt2) + hive + treatment + trt2, random = ~(1|beeID), data = newdf3)
anova(g01$mer, g02$mer) #g02 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g02$mer: NULL
## g01$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g02$mer 10 25152 25210 -12566 25132
## g01$mer 11 25154 25218 -12566 25132 0.1168 1 0.7325summary(g02$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 25104.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3173 -0.4693 0.1882 0.6954 2.3808
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 9.331e+02 3.055e+01
## Xr.0 s(visitNum_centered):trt2Weighted first 0.000e+00 0.000e+00
## Xr s(visitNum_centered):trt2Sham first 1.379e-10 1.174e-05
## Residual 2.355e+03 4.853e+01
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 352.967 7.981 44.23
## Xhive4 -4.248 11.276 -0.38
## XtreatmentWeighted 1.939 3.431 0.57
## Xtrt2Weighted first -10.030 10.478 -0.96
## Xs(visitNum_centered):trt2Sham firstFx1 2.262 1.884 1.20
## Xs(visitNum_centered):trt2Weighted firstFx1 2.583 2.550 1.01
##
## Correlation of Fixed Effects:
## X(Int) Xhive4 XtrtmW Xtr2Wf X(N_):2Sf
## Xhive4 -0.426
## XtrtmntWght -0.242 0.004
## Xtrt2Wghtdf -0.587 -0.012 0.051
## X(N_):2SfF1 0.171 -0.009 -0.707 -0.034
## X(N_):2WfF1 -0.158 -0.002 0.658 0.063 -0.466g03 = gamm4(freq ~ s(visitNum_centered, by = trt2) + hive + trt2, random = ~(1|beeID), data = newdf3)
anova(g02$mer, g03$mer) #g03 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g03$mer: NULL
## g02$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g03$mer 9 25151 25203 -12566 25133
## g02$mer 10 25152 25210 -12566 25132 0.328 1 0.5668summary(g03$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 25109
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3127 -0.4673 0.1923 0.6924 2.3917
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 935.9 30.59
## Xr.0 s(visitNum_centered):trt2Weighted first 0.0 0.00
## Xr s(visitNum_centered):trt2Sham first 0.0 0.00
## Residual 2354.1 48.52
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 354.059 7.754 45.66
## Xhive4 -4.271 11.292 -0.38
## Xtrt2Weighted first -10.330 10.479 -0.99
## Xs(visitNum_centered):trt2Sham firstFx1 3.015 1.332 2.26
## Xs(visitNum_centered):trt2Weighted firstFx1 1.635 1.919 0.85
##
## Correlation of Fixed Effects:
## X(Int) Xhive4 Xtr2Wf X(N_):2Sf
## Xhive4 -0.438
## Xtrt2Wghtdf -0.593 -0.012
## X(N_):2SfF1 0.000 -0.008 0.003
## X(N_):2WfF1 0.002 -0.005 0.039 0.000g04 = gamm4(freq ~ s(visitNum_centered, by = trt2) +trt2, random = ~(1|beeID), data = newdf3)
anova(g03$mer, g04$mer) # g04 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g04$mer: NULL
## g03$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g04$mer 8 25149 25195 -12566 25133
## g03$mer 9 25151 25203 -12566 25133 0.1558 1 0.693summary(g04$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 25115.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3139 -0.4690 0.1912 0.6937 2.3917
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 9.112e+02 3.019e+01
## Xr.0 s(visitNum_centered):trt2Weighted first 1.513e-09 3.890e-05
## Xr s(visitNum_centered):trt2Sham first 3.322e-12 1.823e-06
## Residual 2.354e+03 4.852e+01
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 352.774 6.883 51.25
## Xtrt2Weighted first -10.376 10.345 -1.00
## Xs(visitNum_centered):trt2Sham firstFx1 3.008 1.332 2.26
## Xs(visitNum_centered):trt2Weighted firstFx1 1.631 1.919 0.85
##
## Correlation of Fixed Effects:
## X(Int) Xtr2Wf X(N_):2Sf
## Xtrt2Wghtdf -0.665
## X(N_):2SfF1 -0.004 0.003
## X(N_):2WfF1 0.000 0.039 0.000g05 = gamm4(freq ~ s(visitNum_centered) +trt2, random = ~(1|beeID), data = newdf3)
anova(g04$mer, g05$mer) # g05 slightly better (according to BIC)## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g05$mer: NULL
## g04$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g05$mer 6 25145 25180 -12567 25133
## g04$mer 8 25149 25195 -12566 25133 0.3437 2 0.8421summary(g05$gam)##
## Family: gaussian
## Link function: identity
##
## Formula:
## freq ~ s(visitNum_centered) + trt2
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 352.783 6.875 51.312 <2e-16 ***
## trt2Weighted first -10.188 10.329 -0.986 0.324
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered) 1 1 5.478 0.0193 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = -0.00388
## lmer.REML = 25120 Scale est. = 2353.5 n = 2360g06 = gamm4(freq ~ s(visitNum_centered), random = ~(1|beeID), data = newdf3)
anova(g05$mer, g06$mer) # g05 slightly better (according to BIC)## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g06$mer: NULL
## g05$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g06$mer 5 25144 25173 -12567 25134
## g05$mer 6 25145 25180 -12567 25133 1.0153 1 0.3136summary(g06$mer) # g06 Better## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 25127.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3036 -0.4740 0.1917 0.6901 2.3998
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 9.078e+02 3.013e+01
## Xr s(visitNum_centered) 9.414e-11 9.703e-06
## Residual 2.354e+03 4.851e+01
## Number of obs: 2360, groups: beeID, 36; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 348.268 5.127 67.93
## Xs(visitNum_centered)Fx1 2.587 1.093 2.37
##
## Correlation of Fixed Effects:
## X(Int)
## Xs(vstN_)F1 0.018g07 = gamm4(freq ~ 1, random = ~(1|beeID), data = newdf3)
anova(g06$mer, g07$mer) # g07 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g07$mer: NULL
## g06$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g07$mer 3 25146 25163 -12570 25140
## g06$mer 5 25144 25173 -12567 25134 5.584 2 0.0613 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# looks like GAMM is not necessary -- no predictors significantly affect frequencyModeling frequency with lmer
Do a similar thing to GAMM above (but make it more interpretable)
# fit lmer that is similar to gamm above
# interaction that may be important, based on domain knowledge
m0 = lmer(freq ~ I(scale(visitNum_centered)) * trt2 + I(scale(IT)) * treatment + hive + I(scale(visitNum_centered^2)) + I(scale(IT)^2) + (1|beeID), data = newdf3, REML = FALSE)
summary(m0)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) * trt2 + I(scale(IT)) * treatment +
## hive + I(scale(visitNum_centered^2)) + I(scale(IT)^2) + (1 |
## beeID)
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25151.7 25220.8 -12563.8 25127.7 2348
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2909 -0.4690 0.2002 0.6886 2.3918
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 812.4 28.50
## Residual 2348.7 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 356.7188 8.2319 43.33
## I(scale(visitNum_centered)) 1.3722 2.4815 0.55
## trt2Weighted first -9.6850 9.9725 -0.97
## I(scale(IT)) -4.9677 5.4807 -0.91
## treatmentWeighted 2.9453 3.7036 0.80
## hive4 -4.9106 10.5727 -0.46
## I(scale(visitNum_centered^2)) 0.1972 1.5799 0.12
## I(scale(IT)^2) -5.2727 3.9217 -1.34
## I(scale(visitNum_centered)):trt2Weighted first 1.1188 4.2882 0.26
## I(scale(IT)):treatmentWeighted 3.8345 2.2161 1.73
##
## Correlation of Fixed Effects:
## (Intr) I((N_) trt2Wf I(s(IT)) trtmnW hive4 I((N_^ I((IT)^
## I(scl(vN_)) 0.192
## trt2Wghtdfr -0.504 -0.048
## I(scal(IT)) -0.062 0.040 0.150
## trtmntWghtd -0.257 -0.742 0.061 -0.034
## hive4 -0.411 -0.020 -0.017 -0.005 0.011
## I(sc(N_^2)) -0.071 -0.623 0.032 -0.036 0.350 0.016
## I(sc(IT)^2) -0.400 -0.009 -0.068 0.128 0.007 0.059 -0.036
## I((N_)):2Wf -0.214 -0.842 0.070 -0.015 0.821 0.013 0.448 0.018
## I(sc(IT)):W -0.034 -0.171 -0.001 -0.236 0.136 0.005 -0.026 -0.029
## I((N_f
## I(scl(vN_))
## trt2Wghtdfr
## I(scal(IT))
## trtmntWghtd
## hive4
## I(sc(N_^2))
## I(sc(IT)^2)
## I((N_)):2Wf
## I(sc(IT)):W 0.088# no interaction
m1 = update(m0, .~. - I(scale(visitNum_centered^2)))
BIC(m0, m1) # stay with m1 -- no interaction## df BIC
## m0 12 25220.85
## m1 11 25213.10anova(m0, m1) # agrees with BIC## Data: newdf3
## Models:
## m1: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m1: hive + I(scale(IT)^2) + (1 | beeID) + I(scale(visitNum_centered)):trt2 +
## m1: I(scale(IT)):treatment
## m0: freq ~ I(scale(visitNum_centered)) * trt2 + I(scale(IT)) * treatment +
## m0: hive + I(scale(visitNum_centered^2)) + I(scale(IT)^2) + (1 |
## m0: beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m1 11 25150 25213 -12564 25128
## m0 12 25152 25221 -12564 25128 0.0156 1 0.9007summary(m1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## hive + I(scale(IT)^2) + (1 | beeID) + I(scale(visitNum_centered)):trt2 +
## I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25149.7 25213.1 -12563.8 25127.7 2349
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2901 -0.4672 0.1999 0.6872 2.3924
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 812.2 28.50
## Residual 2348.7 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 356.792 8.210 43.46
## I(scale(visitNum_centered)) 1.565 1.940 0.81
## trt2Weighted first -9.725 9.966 -0.98
## I(scale(IT)) -4.943 5.477 -0.90
## treatmentWeighted 2.784 3.470 0.80
## hive4 -4.932 10.570 -0.47
## I(scale(IT)^2) -5.255 3.919 -1.34
## I(scale(visitNum_centered)):trt2Weighted first 0.879 3.833 0.23
## I(scale(IT)):treatmentWeighted 3.842 2.215 1.73
##
## Correlation of Fixed Effects:
## (Intr) I((N_) trt2Wf I(s(IT)) trtmnW hive4 I((IT)^ I((N_f
## I(scl(vN_)) 0.190
## trt2Wghtdfr -0.503 -0.036
## I(scal(IT)) -0.064 0.023 0.152
## trtmntWghtd -0.248 -0.716 0.053 -0.022
## hive4 -0.411 -0.013 -0.018 -0.005 0.006
## I(sc(IT)^2) -0.404 -0.040 -0.067 0.127 0.021 0.060
## I((N_)):2Wf -0.204 -0.805 0.062 0.001 0.793 0.006 0.038
## I(sc(IT)):W -0.036 -0.239 0.000 -0.237 0.155 0.005 -0.030 0.111m1.1 <- update(m1, .~. - I(scale(visitNum_centered)):trt2)
anova(m1.1, m1) # keep 1.1## Data: newdf3
## Models:
## m1.1: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m1.1: hive + I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## m1: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m1: hive + I(scale(IT)^2) + (1 | beeID) + I(scale(visitNum_centered)):trt2 +
## m1: I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m1.1 10 25148 25205 -12564 25128
## m1 11 25150 25213 -12564 25128 0.0526 1 0.8187summary(m1.1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## hive + I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25147.7 25205.4 -12563.9 25127.7 2350
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2923 -0.4665 0.2003 0.6857 2.3925
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 812.7 28.51
## Residual 2348.7 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 357.176 8.039 44.43
## I(scale(visitNum_centered)) 1.923 1.152 1.67
## trt2Weighted first -9.867 9.950 -0.99
## I(scale(IT)) -4.945 5.478 -0.90
## treatmentWeighted 2.153 2.113 1.02
## hive4 -4.947 10.573 -0.47
## I(scale(IT)^2) -5.289 3.917 -1.35
## I(scale(IT)):treatmentWeighted 3.785 2.202 1.72
##
## Correlation of Fixed Effects:
## (Intr) I((N_) trt2Wf I(s(IT)) trtmnW hive4 I((IT)^
## I(scl(vN_)) 0.043
## trt2Wghtdfr -0.502 0.024
## I(scal(IT)) -0.066 0.040 0.152
## trtmntWghtd -0.144 -0.214 0.006 -0.039
## hive4 -0.419 -0.013 -0.018 -0.005 0.002
## I(sc(IT)^2) -0.405 -0.017 -0.070 0.127 -0.015 0.060
## I(sc(IT)):W -0.014 -0.253 -0.007 -0.239 0.111 0.005 -0.034m2 <- update(m1.1, .~. - hive)
anova(m1.1, m2) # keep m2 (based on BIC)## Data: newdf3
## Models:
## m2: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m2: I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## m1.1: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m1.1: hive + I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m2 9 25146 25198 -12564 25128
## m1.1 10 25148 25205 -12564 25128 0.2182 1 0.6404summary(m2)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25145.9 25197.8 -12564.0 25127.9 2351
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2954 -0.4655 0.2005 0.6868 2.3943
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 818 28.60
## Residual 2349 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 355.602 7.323 48.56
## I(scale(visitNum_centered)) 1.916 1.152 1.66
## trt2Weighted first -9.951 9.979 -1.00
## I(scale(IT)) -4.957 5.494 -0.90
## treatmentWeighted 2.154 2.113 1.02
## I(scale(IT)^2) -5.179 3.922 -1.32
## I(scale(IT)):treatmentWeighted 3.791 2.202 1.72
##
## Correlation of Fixed Effects:
## (Intr) I((N_) trt2Wf I(s(IT)) trtmnW I((IT)^
## I(scl(vN_)) 0.041
## trt2Wghtdfr -0.561 0.023
## I(scal(IT)) -0.074 0.040 0.152
## trtmntWghtd -0.158 -0.214 0.006 -0.039
## I(sc(IT)^2) -0.419 -0.016 -0.069 0.127 -0.015
## I(sc(IT)):W -0.013 -0.253 -0.007 -0.238 0.111 -0.034m3 <- update(m2, .~. - I(scale(IT)^2))
anova(m2, m3) # keep m3## Data: newdf3
## Models:
## m3: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m3: (1 | beeID) + I(scale(IT)):treatment
## m2: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m2: I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m3 8 25146 25192 -12565 25130
## m2 9 25146 25198 -12564 25128 1.7007 1 0.1922summary(m3)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## (1 | beeID) + I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25145.6 25191.8 -12564.8 25129.6 2352
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2974 -0.4648 0.1939 0.6878 2.3993
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 860.5 29.33
## Residual 2348.7 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 351.549 6.806 51.65
## I(scale(visitNum_centered)) 1.895 1.152 1.65
## trt2Weighted first -10.862 10.199 -1.06
## I(scale(IT)) -4.037 5.576 -0.72
## treatmentWeighted 2.113 2.113 1.00
## I(scale(IT)):treatmentWeighted 3.701 2.201 1.68
##
## Correlation of Fixed Effects:
## (Intr) I((N_) trt2Wf I(s(IT)) trtmnW
## I(scl(vN_)) 0.038
## trt2Wghtdfr -0.652 0.022
## I(scal(IT)) -0.024 0.041 0.162
## trtmntWghtd -0.176 -0.214 0.004 -0.036
## I(sc(IT)):W -0.029 -0.254 -0.009 -0.230 0.110m3.1 <- update(m3, .~. - trt2)
anova(m3, m3.1) # keep m3.1## Data: newdf3
## Models:
## m3.1: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + treatment +
## m3.1: (1 | beeID) + I(scale(IT)):treatment
## m3: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m3: (1 | beeID) + I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m3.1 7 25145 25185 -12565 25131
## m3 8 25146 25192 -12565 25130 1.1172 1 0.2905summary(m3.1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + treatment +
## (1 | beeID) + I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25144.8 25185.1 -12565.4 25130.8 2353
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3023 -0.4645 0.1920 0.6862 2.3959
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 888.4 29.81
## Residual 2348.7 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 346.822 5.236 66.24
## I(scale(visitNum_centered)) 1.922 1.152 1.67
## I(scale(IT)) -3.075 5.583 -0.55
## treatmentWeighted 2.123 2.113 1.00
## I(scale(IT)):treatmentWeighted 3.686 2.201 1.68
##
## Correlation of Fixed Effects:
## (Intr) I((N_) I(s(IT)) trtmnW
## I(scl(vN_)) 0.067
## I(scal(IT)) 0.109 0.038
## trtmntWghtd -0.226 -0.215 -0.037
## I(sc(IT)):W -0.046 -0.254 -0.228 0.111m4 <- update(m3.1, .~. - treatment)
anova(m3.1, m4) #keep m4## Data: newdf3
## Models:
## m4: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID) +
## m4: I(scale(IT)):treatment
## m3.1: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + treatment +
## m3.1: (1 | beeID) + I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m4 6 25144 25178 -12566 25132
## m3.1 7 25145 25185 -12565 25131 1.0089 1 0.3152summary(m4)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID) +
## I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25143.8 25178.4 -12565.9 25131.8 2354
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2783 -0.4565 0.1932 0.6827 2.4222
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 888.5 29.81
## Residual 2349.7 48.47
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.008 5.102 68.22
## I(scale(visitNum_centered)) 2.171 1.125 1.93
## I(scale(IT)) -2.868 5.580 -0.51
## I(scale(IT)):treatmentWeighted 3.442 2.188 1.57
##
## Correlation of Fixed Effects:
## (Intr) I((N_) I(s(IT))
## I(scl(vN_)) 0.020
## I(scal(IT)) 0.104 0.031
## I(sc(IT)):W -0.022 -0.237 -0.226m5 <- update(m4, .~. -I(scale(IT)):treatment)
anova(m4, m5) # keep m5 -- baesd on BIC (agrees with GAMM analysis above)## Data: newdf3
## Models:
## m5: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID)
## m4: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID) +
## m4: I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m5 5 25144 25173 -12567 25134
## m4 6 25144 25178 -12566 25132 2.4726 1 0.1158summary(m5)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID)
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25144.2 25173.1 -12567.1 25134.2 2355
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3038 -0.4736 0.1929 0.6902 2.3985
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 880.5 29.67
## Residual 2352.5 48.50
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.1844 5.0783 68.56
## I(scale(visitNum_centered)) 2.5898 1.0937 2.37
## I(scale(IT)) -0.8855 5.4117 -0.16
##
## Correlation of Fixed Effects:
## (Intr) I((N_)
## I(scl(vN_)) 0.015
## I(scal(IT)) 0.102 -0.024m6 <- update(m5, .~. - I(scale(IT)))
anova(m5, m6)## Data: newdf3
## Models:
## m6: freq ~ I(scale(visitNum_centered)) + (1 | beeID)
## m5: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m6 4 25142 25165 -12567 25134
## m5 5 25144 25173 -12567 25134 0.0268 1 0.8701summary(m6) ## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: freq ~ I(scale(visitNum_centered)) + (1 | beeID)
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25142.3 25165.3 -12567.1 25134.3 2356
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3033 -0.4735 0.1920 0.6906 2.3989
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 881.3 29.69
## Residual 2352.5 48.50
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.269 5.054 68.91
## I(scale(visitNum_centered)) 2.586 1.093 2.36
##
## Correlation of Fixed Effects:
## (Intr)
## I(scl(vN_)) 0.018m7 <- update(m6, .~. - I(scale(visitNum_centered)))
anova(m6, m7) # keep m7## Data: newdf3
## Models:
## m7: freq ~ (1 | beeID)
## m6: freq ~ I(scale(visitNum_centered)) + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m7 3 25146 25163 -12570 25140
## m6 4 25142 25165 -12567 25134 5.584 1 0.01813 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(m7)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: freq ~ (1 | beeID)
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25145.8 25163.1 -12569.9 25139.8 2357
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3391 -0.4568 0.1808 0.6925 2.3602
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 875.4 29.59
## Residual 2358.4 48.56
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.056 5.037 69.09# get p-value for treament for paper
m_trt <- update(m7, .~. + treatment)
anova(m7, m_trt) # p-val for paper## Data: newdf3
## Models:
## m7: freq ~ (1 | beeID)
## m_trt: freq ~ (1 | beeID) + treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m7 3 25146 25163 -12570 25140
## m_trt 4 25146 25169 -12569 25138 1.5992 1 0.206m_IT <- update(m7, .~. + IT)
anova(m7, m_IT) # p-val for IT span## Data: newdf3
## Models:
## m7: freq ~ (1 | beeID)
## m_IT: freq ~ (1 | beeID) + IT
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m7 3 25146 25163 -12570 25140
## m_IT 4 25148 25171 -12570 25140 0.0114 1 0.9151# final freq mod for paper
finmod <- update(m7, .~., REML = TRUE)
summary(finmod) # final model for paper -- same as gamm## Linear mixed model fit by REML ['lmerMod']
## Formula: freq ~ (1 | beeID)
## Data: newdf3
##
## REML criterion at convergence: 25134.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3401 -0.4580 0.1806 0.6919 2.3616
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 901.6 30.03
## Residual 2358.4 48.56
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.056 5.109 68.12summary(finmod) # summary for paper -- no predictors predict frequency (when accounting for beeID)## Linear mixed model fit by REML ['lmerMod']
## Formula: freq ~ (1 | beeID)
## Data: newdf3
##
## REML criterion at convergence: 25134.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3401 -0.4580 0.1806 0.6919 2.3616
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 901.6 30.03
## Residual 2358.4 48.56
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.056 5.109 68.12plot(finmod)
qqnorm(ranef(finmod)$beeID[[1]])
qqline(ranef(finmod)$beeID[[1]])
sjp.lmer(finmod, type = "re", sort = TRUE) # plot random effects to find any outliers## Plotting random effects...
# sjp.lmer(finmod, type = 'fe', sort = TRUE, p.kr = FALSE) # plot fixed effectsBootstrap CI’s for figure for paper
# set number of bootstrap replicates for models
nbootSims = 10000
table(new_df$hive) # more trials from hive 3##
## 3 4
## 1644 716# using hive 3, since it's the one with the most data
# however, hive doesn't affect model anyway
# calculate an average IT for prediction
ITmean = mean(tapply(new_df$IT, INDEX = new_df$beeID, FUN = function(x) x[1] ))
pframe <- expand.grid(trt2 = levels(droplevels(newdf3$trt2)),
IT = ITmean,
visitNum_centered = -50:50,
hive = factor(3, levels = levels(newdf3$hive)),
beeID = 99999,
treatment = levels(newdf3$treatment))
pframe$freq <- 0
pframe <- pframe[(pframe$trt2 == "Sham first" &
pframe$treatment == "Sham" &
pframe$visitNum_centered < 0) |
(pframe$trt2 == "Sham first" &
pframe$treatment == "Weighted" &
pframe$visitNum_centered > 0) |
(pframe$trt2 == "Weighted first" &
pframe$treatment == "Weighted" &
pframe$visitNum_centered < 0) |
(pframe$trt2 == "Weighted first" &
pframe$treatment == "Sham" &
pframe$visitNum_centered > 0)
, ]
# make a model to show the effect of treatment in a plot
m1 <- update(finmod, .~. + treatment)
pp <- predict(m1, newdata = pframe, re.form=NA, type = 'response') # re.form sets all random effects to 0
### Calculate CI's (using bootstrap, not accounting for random effects)
bb2 <- bootMer(m1, FUN=function(x) predict(x, pframe, re.form=NA, type = 'response'), nsim = nbootSims)## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce q
## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce q
## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce q
## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce q
## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce qprint(paste("Number of bootstrap samples", nrow(bb2$t)))## [1] "Number of bootstrap samples 10000"bb2_se <-apply(bb2$t,2,function(x) quantile(x, probs = c(0.025, 0.975)))
pframe$blo<-bb2_se[1,]
pframe$bhi<-bb2_se[2,]
pframe$predMean <- pp
pframe## trt2 IT visitNum_centered hive beeID treatment freq
## 1 Sham first 3.965833 -50 3 99999 Sham 0
## 3 Sham first 3.965833 -49 3 99999 Sham 0
## 5 Sham first 3.965833 -48 3 99999 Sham 0
## 7 Sham first 3.965833 -47 3 99999 Sham 0
## 9 Sham first 3.965833 -46 3 99999 Sham 0
## 11 Sham first 3.965833 -45 3 99999 Sham 0
## 13 Sham first 3.965833 -44 3 99999 Sham 0
## 15 Sham first 3.965833 -43 3 99999 Sham 0
## 17 Sham first 3.965833 -42 3 99999 Sham 0
## 19 Sham first 3.965833 -41 3 99999 Sham 0
## 21 Sham first 3.965833 -40 3 99999 Sham 0
## 23 Sham first 3.965833 -39 3 99999 Sham 0
## 25 Sham first 3.965833 -38 3 99999 Sham 0
## 27 Sham first 3.965833 -37 3 99999 Sham 0
## 29 Sham first 3.965833 -36 3 99999 Sham 0
## 31 Sham first 3.965833 -35 3 99999 Sham 0
## 33 Sham first 3.965833 -34 3 99999 Sham 0
## 35 Sham first 3.965833 -33 3 99999 Sham 0
## 37 Sham first 3.965833 -32 3 99999 Sham 0
## 39 Sham first 3.965833 -31 3 99999 Sham 0
## 41 Sham first 3.965833 -30 3 99999 Sham 0
## 43 Sham first 3.965833 -29 3 99999 Sham 0
## 45 Sham first 3.965833 -28 3 99999 Sham 0
## 47 Sham first 3.965833 -27 3 99999 Sham 0
## 49 Sham first 3.965833 -26 3 99999 Sham 0
## 51 Sham first 3.965833 -25 3 99999 Sham 0
## 53 Sham first 3.965833 -24 3 99999 Sham 0
## 55 Sham first 3.965833 -23 3 99999 Sham 0
## 57 Sham first 3.965833 -22 3 99999 Sham 0
## 59 Sham first 3.965833 -21 3 99999 Sham 0
## 61 Sham first 3.965833 -20 3 99999 Sham 0
## 63 Sham first 3.965833 -19 3 99999 Sham 0
## 65 Sham first 3.965833 -18 3 99999 Sham 0
## 67 Sham first 3.965833 -17 3 99999 Sham 0
## 69 Sham first 3.965833 -16 3 99999 Sham 0
## 71 Sham first 3.965833 -15 3 99999 Sham 0
## 73 Sham first 3.965833 -14 3 99999 Sham 0
## 75 Sham first 3.965833 -13 3 99999 Sham 0
## 77 Sham first 3.965833 -12 3 99999 Sham 0
## 79 Sham first 3.965833 -11 3 99999 Sham 0
## 81 Sham first 3.965833 -10 3 99999 Sham 0
## 83 Sham first 3.965833 -9 3 99999 Sham 0
## 85 Sham first 3.965833 -8 3 99999 Sham 0
## 87 Sham first 3.965833 -7 3 99999 Sham 0
## 89 Sham first 3.965833 -6 3 99999 Sham 0
## 91 Sham first 3.965833 -5 3 99999 Sham 0
## 93 Sham first 3.965833 -4 3 99999 Sham 0
## 95 Sham first 3.965833 -3 3 99999 Sham 0
## 97 Sham first 3.965833 -2 3 99999 Sham 0
## 99 Sham first 3.965833 -1 3 99999 Sham 0
## 104 Weighted first 3.965833 1 3 99999 Sham 0
## 106 Weighted first 3.965833 2 3 99999 Sham 0
## 108 Weighted first 3.965833 3 3 99999 Sham 0
## 110 Weighted first 3.965833 4 3 99999 Sham 0
## 112 Weighted first 3.965833 5 3 99999 Sham 0
## 114 Weighted first 3.965833 6 3 99999 Sham 0
## 116 Weighted first 3.965833 7 3 99999 Sham 0
## 118 Weighted first 3.965833 8 3 99999 Sham 0
## 120 Weighted first 3.965833 9 3 99999 Sham 0
## 122 Weighted first 3.965833 10 3 99999 Sham 0
## 124 Weighted first 3.965833 11 3 99999 Sham 0
## 126 Weighted first 3.965833 12 3 99999 Sham 0
## 128 Weighted first 3.965833 13 3 99999 Sham 0
## 130 Weighted first 3.965833 14 3 99999 Sham 0
## 132 Weighted first 3.965833 15 3 99999 Sham 0
## 134 Weighted first 3.965833 16 3 99999 Sham 0
## 136 Weighted first 3.965833 17 3 99999 Sham 0
## 138 Weighted first 3.965833 18 3 99999 Sham 0
## 140 Weighted first 3.965833 19 3 99999 Sham 0
## 142 Weighted first 3.965833 20 3 99999 Sham 0
## 144 Weighted first 3.965833 21 3 99999 Sham 0
## 146 Weighted first 3.965833 22 3 99999 Sham 0
## 148 Weighted first 3.965833 23 3 99999 Sham 0
## 150 Weighted first 3.965833 24 3 99999 Sham 0
## 152 Weighted first 3.965833 25 3 99999 Sham 0
## 154 Weighted first 3.965833 26 3 99999 Sham 0
## 156 Weighted first 3.965833 27 3 99999 Sham 0
## 158 Weighted first 3.965833 28 3 99999 Sham 0
## 160 Weighted first 3.965833 29 3 99999 Sham 0
## 162 Weighted first 3.965833 30 3 99999 Sham 0
## 164 Weighted first 3.965833 31 3 99999 Sham 0
## 166 Weighted first 3.965833 32 3 99999 Sham 0
## 168 Weighted first 3.965833 33 3 99999 Sham 0
## 170 Weighted first 3.965833 34 3 99999 Sham 0
## 172 Weighted first 3.965833 35 3 99999 Sham 0
## 174 Weighted first 3.965833 36 3 99999 Sham 0
## 176 Weighted first 3.965833 37 3 99999 Sham 0
## 178 Weighted first 3.965833 38 3 99999 Sham 0
## 180 Weighted first 3.965833 39 3 99999 Sham 0
## 182 Weighted first 3.965833 40 3 99999 Sham 0
## 184 Weighted first 3.965833 41 3 99999 Sham 0
## 186 Weighted first 3.965833 42 3 99999 Sham 0
## 188 Weighted first 3.965833 43 3 99999 Sham 0
## 190 Weighted first 3.965833 44 3 99999 Sham 0
## 192 Weighted first 3.965833 45 3 99999 Sham 0
## 194 Weighted first 3.965833 46 3 99999 Sham 0
## 196 Weighted first 3.965833 47 3 99999 Sham 0
## 198 Weighted first 3.965833 48 3 99999 Sham 0
## 200 Weighted first 3.965833 49 3 99999 Sham 0
## 202 Weighted first 3.965833 50 3 99999 Sham 0
## 204 Weighted first 3.965833 -50 3 99999 Weighted 0
## 206 Weighted first 3.965833 -49 3 99999 Weighted 0
## 208 Weighted first 3.965833 -48 3 99999 Weighted 0
## 210 Weighted first 3.965833 -47 3 99999 Weighted 0
## 212 Weighted first 3.965833 -46 3 99999 Weighted 0
## 214 Weighted first 3.965833 -45 3 99999 Weighted 0
## 216 Weighted first 3.965833 -44 3 99999 Weighted 0
## 218 Weighted first 3.965833 -43 3 99999 Weighted 0
## 220 Weighted first 3.965833 -42 3 99999 Weighted 0
## 222 Weighted first 3.965833 -41 3 99999 Weighted 0
## 224 Weighted first 3.965833 -40 3 99999 Weighted 0
## 226 Weighted first 3.965833 -39 3 99999 Weighted 0
## 228 Weighted first 3.965833 -38 3 99999 Weighted 0
## 230 Weighted first 3.965833 -37 3 99999 Weighted 0
## 232 Weighted first 3.965833 -36 3 99999 Weighted 0
## 234 Weighted first 3.965833 -35 3 99999 Weighted 0
## 236 Weighted first 3.965833 -34 3 99999 Weighted 0
## 238 Weighted first 3.965833 -33 3 99999 Weighted 0
## 240 Weighted first 3.965833 -32 3 99999 Weighted 0
## 242 Weighted first 3.965833 -31 3 99999 Weighted 0
## 244 Weighted first 3.965833 -30 3 99999 Weighted 0
## 246 Weighted first 3.965833 -29 3 99999 Weighted 0
## 248 Weighted first 3.965833 -28 3 99999 Weighted 0
## 250 Weighted first 3.965833 -27 3 99999 Weighted 0
## 252 Weighted first 3.965833 -26 3 99999 Weighted 0
## 254 Weighted first 3.965833 -25 3 99999 Weighted 0
## 256 Weighted first 3.965833 -24 3 99999 Weighted 0
## 258 Weighted first 3.965833 -23 3 99999 Weighted 0
## 260 Weighted first 3.965833 -22 3 99999 Weighted 0
## 262 Weighted first 3.965833 -21 3 99999 Weighted 0
## 264 Weighted first 3.965833 -20 3 99999 Weighted 0
## 266 Weighted first 3.965833 -19 3 99999 Weighted 0
## 268 Weighted first 3.965833 -18 3 99999 Weighted 0
## 270 Weighted first 3.965833 -17 3 99999 Weighted 0
## 272 Weighted first 3.965833 -16 3 99999 Weighted 0
## 274 Weighted first 3.965833 -15 3 99999 Weighted 0
## 276 Weighted first 3.965833 -14 3 99999 Weighted 0
## 278 Weighted first 3.965833 -13 3 99999 Weighted 0
## 280 Weighted first 3.965833 -12 3 99999 Weighted 0
## 282 Weighted first 3.965833 -11 3 99999 Weighted 0
## 284 Weighted first 3.965833 -10 3 99999 Weighted 0
## 286 Weighted first 3.965833 -9 3 99999 Weighted 0
## 288 Weighted first 3.965833 -8 3 99999 Weighted 0
## 290 Weighted first 3.965833 -7 3 99999 Weighted 0
## 292 Weighted first 3.965833 -6 3 99999 Weighted 0
## 294 Weighted first 3.965833 -5 3 99999 Weighted 0
## 296 Weighted first 3.965833 -4 3 99999 Weighted 0
## 298 Weighted first 3.965833 -3 3 99999 Weighted 0
## 300 Weighted first 3.965833 -2 3 99999 Weighted 0
## 302 Weighted first 3.965833 -1 3 99999 Weighted 0
## 305 Sham first 3.965833 1 3 99999 Weighted 0
## 307 Sham first 3.965833 2 3 99999 Weighted 0
## 309 Sham first 3.965833 3 3 99999 Weighted 0
## 311 Sham first 3.965833 4 3 99999 Weighted 0
## 313 Sham first 3.965833 5 3 99999 Weighted 0
## 315 Sham first 3.965833 6 3 99999 Weighted 0
## 317 Sham first 3.965833 7 3 99999 Weighted 0
## 319 Sham first 3.965833 8 3 99999 Weighted 0
## 321 Sham first 3.965833 9 3 99999 Weighted 0
## 323 Sham first 3.965833 10 3 99999 Weighted 0
## 325 Sham first 3.965833 11 3 99999 Weighted 0
## 327 Sham first 3.965833 12 3 99999 Weighted 0
## 329 Sham first 3.965833 13 3 99999 Weighted 0
## 331 Sham first 3.965833 14 3 99999 Weighted 0
## 333 Sham first 3.965833 15 3 99999 Weighted 0
## 335 Sham first 3.965833 16 3 99999 Weighted 0
## 337 Sham first 3.965833 17 3 99999 Weighted 0
## 339 Sham first 3.965833 18 3 99999 Weighted 0
## 341 Sham first 3.965833 19 3 99999 Weighted 0
## 343 Sham first 3.965833 20 3 99999 Weighted 0
## 345 Sham first 3.965833 21 3 99999 Weighted 0
## 347 Sham first 3.965833 22 3 99999 Weighted 0
## 349 Sham first 3.965833 23 3 99999 Weighted 0
## 351 Sham first 3.965833 24 3 99999 Weighted 0
## 353 Sham first 3.965833 25 3 99999 Weighted 0
## 355 Sham first 3.965833 26 3 99999 Weighted 0
## 357 Sham first 3.965833 27 3 99999 Weighted 0
## 359 Sham first 3.965833 28 3 99999 Weighted 0
## 361 Sham first 3.965833 29 3 99999 Weighted 0
## 363 Sham first 3.965833 30 3 99999 Weighted 0
## 365 Sham first 3.965833 31 3 99999 Weighted 0
## 367 Sham first 3.965833 32 3 99999 Weighted 0
## 369 Sham first 3.965833 33 3 99999 Weighted 0
## 371 Sham first 3.965833 34 3 99999 Weighted 0
## 373 Sham first 3.965833 35 3 99999 Weighted 0
## 375 Sham first 3.965833 36 3 99999 Weighted 0
## 377 Sham first 3.965833 37 3 99999 Weighted 0
## 379 Sham first 3.965833 38 3 99999 Weighted 0
## 381 Sham first 3.965833 39 3 99999 Weighted 0
## 383 Sham first 3.965833 40 3 99999 Weighted 0
## 385 Sham first 3.965833 41 3 99999 Weighted 0
## 387 Sham first 3.965833 42 3 99999 Weighted 0
## 389 Sham first 3.965833 43 3 99999 Weighted 0
## 391 Sham first 3.965833 44 3 99999 Weighted 0
## 393 Sham first 3.965833 45 3 99999 Weighted 0
## 395 Sham first 3.965833 46 3 99999 Weighted 0
## 397 Sham first 3.965833 47 3 99999 Weighted 0
## 399 Sham first 3.965833 48 3 99999 Weighted 0
## 401 Sham first 3.965833 49 3 99999 Weighted 0
## 403 Sham first 3.965833 50 3 99999 Weighted 0
## blo bhi predMean
## 1 336.4795 356.5832 346.6421
## 3 336.4795 356.5832 346.6421
## 5 336.4795 356.5832 346.6421
## 7 336.4795 356.5832 346.6421
## 9 336.4795 356.5832 346.6421
## 11 336.4795 356.5832 346.6421
## 13 336.4795 356.5832 346.6421
## 15 336.4795 356.5832 346.6421
## 17 336.4795 356.5832 346.6421
## 19 336.4795 356.5832 346.6421
## 21 336.4795 356.5832 346.6421
## 23 336.4795 356.5832 346.6421
## 25 336.4795 356.5832 346.6421
## 27 336.4795 356.5832 346.6421
## 29 336.4795 356.5832 346.6421
## 31 336.4795 356.5832 346.6421
## 33 336.4795 356.5832 346.6421
## 35 336.4795 356.5832 346.6421
## 37 336.4795 356.5832 346.6421
## 39 336.4795 356.5832 346.6421
## 41 336.4795 356.5832 346.6421
## 43 336.4795 356.5832 346.6421
## 45 336.4795 356.5832 346.6421
## 47 336.4795 356.5832 346.6421
## 49 336.4795 356.5832 346.6421
## 51 336.4795 356.5832 346.6421
## 53 336.4795 356.5832 346.6421
## 55 336.4795 356.5832 346.6421
## 57 336.4795 356.5832 346.6421
## 59 336.4795 356.5832 346.6421
## 61 336.4795 356.5832 346.6421
## 63 336.4795 356.5832 346.6421
## 65 336.4795 356.5832 346.6421
## 67 336.4795 356.5832 346.6421
## 69 336.4795 356.5832 346.6421
## 71 336.4795 356.5832 346.6421
## 73 336.4795 356.5832 346.6421
## 75 336.4795 356.5832 346.6421
## 77 336.4795 356.5832 346.6421
## 79 336.4795 356.5832 346.6421
## 81 336.4795 356.5832 346.6421
## 83 336.4795 356.5832 346.6421
## 85 336.4795 356.5832 346.6421
## 87 336.4795 356.5832 346.6421
## 89 336.4795 356.5832 346.6421
## 91 336.4795 356.5832 346.6421
## 93 336.4795 356.5832 346.6421
## 95 336.4795 356.5832 346.6421
## 97 336.4795 356.5832 346.6421
## 99 336.4795 356.5832 346.6421
## 104 336.4795 356.5832 346.6421
## 106 336.4795 356.5832 346.6421
## 108 336.4795 356.5832 346.6421
## 110 336.4795 356.5832 346.6421
## 112 336.4795 356.5832 346.6421
## 114 336.4795 356.5832 346.6421
## 116 336.4795 356.5832 346.6421
## 118 336.4795 356.5832 346.6421
## 120 336.4795 356.5832 346.6421
## 122 336.4795 356.5832 346.6421
## 124 336.4795 356.5832 346.6421
## 126 336.4795 356.5832 346.6421
## 128 336.4795 356.5832 346.6421
## 130 336.4795 356.5832 346.6421
## 132 336.4795 356.5832 346.6421
## 134 336.4795 356.5832 346.6421
## 136 336.4795 356.5832 346.6421
## 138 336.4795 356.5832 346.6421
## 140 336.4795 356.5832 346.6421
## 142 336.4795 356.5832 346.6421
## 144 336.4795 356.5832 346.6421
## 146 336.4795 356.5832 346.6421
## 148 336.4795 356.5832 346.6421
## 150 336.4795 356.5832 346.6421
## 152 336.4795 356.5832 346.6421
## 154 336.4795 356.5832 346.6421
## 156 336.4795 356.5832 346.6421
## 158 336.4795 356.5832 346.6421
## 160 336.4795 356.5832 346.6421
## 162 336.4795 356.5832 346.6421
## 164 336.4795 356.5832 346.6421
## 166 336.4795 356.5832 346.6421
## 168 336.4795 356.5832 346.6421
## 170 336.4795 356.5832 346.6421
## 172 336.4795 356.5832 346.6421
## 174 336.4795 356.5832 346.6421
## 176 336.4795 356.5832 346.6421
## 178 336.4795 356.5832 346.6421
## 180 336.4795 356.5832 346.6421
## 182 336.4795 356.5832 346.6421
## 184 336.4795 356.5832 346.6421
## 186 336.4795 356.5832 346.6421
## 188 336.4795 356.5832 346.6421
## 190 336.4795 356.5832 346.6421
## 192 336.4795 356.5832 346.6421
## 194 336.4795 356.5832 346.6421
## 196 336.4795 356.5832 346.6421
## 198 336.4795 356.5832 346.6421
## 200 336.4795 356.5832 346.6421
## 202 336.4795 356.5832 346.6421
## 204 339.0374 359.2846 349.2520
## 206 339.0374 359.2846 349.2520
## 208 339.0374 359.2846 349.2520
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## 403 339.0374 359.2846 349.2520### Make frequency plots for paper
# predictions are from this model
summary(m1)## Linear mixed model fit by REML ['lmerMod']
## Formula: freq ~ (1 | beeID) + treatment
## Data: newdf3
##
## REML criterion at convergence: 25129.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3673 -0.4740 0.1874 0.6837 2.3307
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 901.5 30.02
## Residual 2357.8 48.56
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 346.642 5.230 66.28
## treatmentWeighted 2.610 2.064 1.26
##
## Correlation of Fixed Effects:
## (Intr)
## trtmntWghtd -0.214anova(m1, update(m1, .~. - treatment)) #p-val and BIC for paper## refitting model(s) with ML (instead of REML)## Data: newdf3
## Models:
## update(m1, . ~ . - treatment): freq ~ (1 | beeID)
## m1: freq ~ (1 | beeID) + treatment
## Df AIC BIC logLik deviance Chisq Chi Df
## update(m1, . ~ . - treatment) 3 25146 25163 -12570 25140
## m1 4 25146 25169 -12569 25138 1.5992 1
## Pr(>Chisq)
## update(m1, . ~ . - treatment)
## m1 0.206pframe$trt3 <- mapvalues(pframe$trt2, from = c("Sham first", "Weighted first"),
to = c("Sham -> Weighted", "Weighted -> Sham"))
g0 <- ggplot(pframe, aes(x=visitNum_centered, y=predMean))+
geom_line(aes(color = treatment))+
labs(y = "Sonication frequency (Hz)", x = "Sonication number\n (0 is when treatment switched)") +
geom_ribbon(aes(x = visitNum_centered, ymin = blo, ymax = bhi, fill= treatment), alpha = 0.2) +
facet_wrap(~trt3) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
scale_fill_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = c(0.5, 0.90),
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal") +
ylim(c(330, 370))
g0
ggsave(filename = file.path(figDir, "WeightedSham_Freq_Timeseries.pdf"), width =5, height = 3.6)
g1 <- g0 + geom_point(data = newdf3[newdf3$visitNum_centered < 50,],
aes(x = visitNum_centered, y = freq), position = position_jitter(height = 5), size = 0.1, pch = 16, alpha = 0.4) +
ylim(c(220, 470))## Scale for 'y' is already present. Adding another scale for 'y', which
## will replace the existing scale.g1 # note that the distribution of frequency is a bit bimodal -- this could be 
# a problem, so we ran the analysis with a freq cutoff at 270
# we found no significant differences in the models either way.
ggsave(filename = file.path(figDir, "WeightedSham_Freq_Timeseries_RawData.pdf"), width =5, height = 3.6)
g1 <- g0 + geom_point(data = newdf3[newdf3$visitNum_centered < 50,],
aes(x = visitNum_centered, y = freq), position = position_jitter(height = 5), size = 0.1, pch = 16, alpha = 0.4) +
ylim(c(270, 480))## Scale for 'y' is already present. Adding another scale for 'y', which
## will replace the existing scale.g1## Warning: Removed 741 rows containing missing values (geom_point).
ggsave(filename = file.path(figDir, "WeightedSham_Freq_Timeseries_RawData_trimmed.pdf"), width =5, height = 3.6)## Warning: Removed 733 rows containing missing values (geom_point).# mean and 95% CI (without visit number)
g0_freq <- ggplot(pframe[pframe$visitNum_centered %in% c(-25, 25), ], aes(x=treatment, y=predMean))+
geom_point(aes(color = treatment), alpha = 1) +
labs(y = "Sonication frequency (Hz)", x = "Flower treatment") +
geom_errorbar(aes(x = treatment, ymin = blo, ymax = bhi, color= treatment), alpha = 1, width = 0.1) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0, end = 0, option = "A") +
theme(legend.position = "none",
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0_freq
ggsave(filename = file.path(figDir, "WeightedSham_Freq_pointWhiskers_BW.pdf"), width =2.5, height = 3)
g0 <- ggplot(pframe[pframe$visitNum_centered %in% c(-25, 25), ], aes(x=treatment, y=predMean))+
geom_point(aes(color = treatment), alpha = 1) +
labs(y = "Sonication frequency (Hz)", x = "Flower treatment") +
geom_errorbar(aes(x = treatment, ymin = blo, ymax = bhi, color= treatment), alpha = 1, width = 0.1) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = "none",
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0
ggsave(filename = file.path(figDir, "WeightedSham_Freq_pointWhiskers.pdf"), width =5, height = 3.6)
Fig2a <- g0
## add raw data
g1 <- g0 + geom_point(data = newdf3, aes(x = treatment, y = freq, color = treatment), position = position_jitter(width = 0.1, height = 6), alpha = 0.4, pch = 16, size = 0.2)
g1
ggsave(filename = file.path(figDir, "WeightedSham_Freq_pointWhiskers_rawData.pdf"), width =5, height = 3.6)
# "Mean and bootstrap CI based on fixed-effects uncertainty ONLY"
g0 <- ggplot(pframe, aes(x=visitNum_centered, y=predMean))+
geom_point()+
labs(y = "Sonication frequency (Hz)", x = "buzzNumber") +
geom_ribbon(aes(x = visitNum_centered, ymin = blo, ymax = bhi), alpha = 0.2) +
facet_wrap(~trt2)
g0
# plot effect to see if it agrees
plot(Effect(c("treatment"), m1))
Modeling amplitude with gamm
g01 = gamm4(log(amp_acc) ~ s(visitNum_centered, by = trt2) + trt2 + IT + hive + treatment, random = ~(1|beeID), data = newdf3)
par(mfrow = c(2,3))
aab <- plot(g01$gam, all.terms = TRUE, rug = FALSE, shade = TRUE)
summary(g01$gam) # Summary for paper ##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(amp_acc) ~ s(visitNum_centered, by = trt2) + trt2 + IT +
## hive + treatment
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.72977 0.58219 4.689 2.90e-06 ***
## trt2Weighted first -0.05297 0.09833 -0.539 0.590
## IT 0.21347 0.14365 1.486 0.137
## hive4 0.09955 0.10391 0.958 0.338
## treatmentWeighted -0.32857 0.04921 -6.678 3.02e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered):trt2Sham first 1.414 1.414 4.924 0.0175 *
## s(visitNum_centered):trt2Weighted first 2.800 2.800 3.683 0.0323 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0571
## lmer.REML = 4557.5 Scale est. = 0.384 n = 2360summary(g01$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4557.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9897 -0.5342 0.1125 0.6707 2.6828
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.076179 0.27601
## Xr.0 s(visitNum_centered):trt2Weighted first 0.376254 0.61340
## Xr s(visitNum_centered):trt2Sham first 0.008701 0.09328
## Residual 0.384002 0.61968
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 2.729772 0.582186 4.689
## Xtrt2Weighted first -0.052966 0.098331 -0.539
## XIT 0.213470 0.143651 1.486
## Xhive4 0.099547 0.103913 0.958
## XtreatmentWeighted -0.328574 0.049206 -6.678
## Xs(visitNum_centered):trt2Sham firstFx1 0.059922 0.036356 1.648
## Xs(visitNum_centered):trt2Weighted firstFx1 0.003639 0.188745 0.019
##
## Correlation of Fixed Effects:
## X(Int) Xtr2Wf XIT Xhive4 XtrtmW X(N_):2Sf
## Xtrt2Wghtdf -0.238
## XIT -0.991 0.166
## Xhive4 -0.041 -0.011 -0.012
## XtrtmntWght -0.062 0.061 0.015 0.000
## X(N_):2SfF1 0.051 -0.029 -0.030 -0.003 -0.455
## X(N_):2WfF1 -0.001 0.060 0.000 0.001 0.023 -0.011dev.off()## null device
## 1g011 = gamm4(log(amp_acc) ~ s(visitNum_centered, by = trt2) + IT + hive + treatment, random = ~(1|beeID), data = newdf3)
par(mfrow = c(2,3))
aab <- plot(g011$gam, all.terms = TRUE, rug = FALSE, shade = TRUE)
summary(g011$gam) ##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(amp_acc) ~ s(visitNum_centered, by = trt2) + IT + hive +
## treatment
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.65539 0.55974 4.744 2.22e-06 ***
## IT 0.22614 0.14023 1.613 0.107
## hive4 0.09890 0.10286 0.961 0.336
## treatmentWeighted -0.32629 0.04905 -6.652 3.58e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered):trt2Sham first 1.396 1.396 4.868 0.0185 *
## s(visitNum_centered):trt2Weighted first 2.824 2.824 3.711 0.0286 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0543
## lmer.REML = 4555 Scale est. = 0.38399 n = 2360summary(g011$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4555
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9904 -0.5310 0.1120 0.6721 2.6775
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.074527 0.27300
## Xr.0 s(visitNum_centered):trt2Weighted first 0.387226 0.62227
## Xr s(visitNum_centered):trt2Sham first 0.008222 0.09068
## Residual 0.383989 0.61967
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 2.65539 0.55974 4.744
## XIT 0.22614 0.14023 1.613
## Xhive4 0.09890 0.10286 0.961
## XtreatmentWeighted -0.32629 0.04905 -6.652
## Xs(visitNum_centered):trt2Sham firstFx1 0.05943 0.03583 1.659
## Xs(visitNum_centered):trt2Weighted firstFx1 0.01018 0.19078 0.053
##
## Correlation of Fixed Effects:
## X(Int) XIT Xhive4 XtrtmW X(N_):2Sf
## XIT -0.994
## Xhive4 -0.045 -0.011
## XtrtmntWght -0.049 0.005 0.001
## X(N_):2SfF1 0.046 -0.026 -0.003 -0.463
## X(N_):2WfF1 0.014 -0.010 0.002 0.018 -0.008dev.off()## null device
## 1anova(g01$mer, g011$mer) # go with g011## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g011$mer: NULL
## g01$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g011$mer 10 4553.4 4611.1 -2266.7 4533.4
## g01$mer 11 4555.1 4618.5 -2266.5 4533.1 0.3497 1 0.5543g02 = gamm4(log(amp_acc) ~ s(visitNum_centered, by = trt2) + IT + treatment, random = ~(1|beeID), data = newdf3)
par(mfrow = c(2,3))
aab <- plot(g02$gam, all.terms = TRUE, rug = FALSE, shade = TRUE)
summary(g02$gam) # Summary for paper ##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(amp_acc) ~ s(visitNum_centered, by = trt2) + IT + treatment
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.67960 0.55806 4.802 1.67e-06 ***
## IT 0.22770 0.13995 1.627 0.104
## treatmentWeighted -0.32686 0.04912 -6.655 3.52e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered):trt2Sham first 1.412 1.412 4.868 0.0182 *
## s(visitNum_centered):trt2Weighted first 2.810 2.810 3.669 0.0310 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0534
## lmer.REML = 4553.2 Scale est. = 0.384 n = 2360summary(g02$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4553.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9949 -0.5328 0.1143 0.6739 2.6875
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.074211 0.27242
## Xr.0 s(visitNum_centered):trt2Weighted first 0.379482 0.61602
## Xr s(visitNum_centered):trt2Sham first 0.008663 0.09308
## Residual 0.384001 0.61968
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 2.679603 0.558065 4.802
## XIT 0.227704 0.139951 1.627
## XtreatmentWeighted -0.326857 0.049116 -6.655
## Xs(visitNum_centered):trt2Sham firstFx1 0.059463 0.036299 1.638
## Xs(visitNum_centered):trt2Weighted firstFx1 0.009651 0.189097 0.051
##
## Correlation of Fixed Effects:
## X(Int) XIT XtrtmW X(N_):2Sf
## XIT -0.995
## XtrtmntWght -0.049 0.005
## X(N_):2SfF1 0.046 -0.026 -0.455
## X(N_):2WfF1 0.014 -0.010 0.019 -0.009dev.off()## null device
## 1anova(g011$mer, g02$mer) # g02 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g02$mer: NULL
## g011$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g02$mer 9 4552.4 4604.3 -2267.2 4534.4
## g011$mer 10 4553.4 4611.1 -2266.7 4533.4 0.9778 1 0.3228g03 = gamm4(log(amp_acc) ~ s(visitNum_centered, by = trt2) + treatment, random = ~(1|beeID), data = newdf3)
anova(g02$mer, g03$mer) #keep g03## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g03$mer: NULL
## g02$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g03$mer 8 4553.1 4599.2 -2268.5 4537.1
## g02$mer 9 4552.4 4604.3 -2267.2 4534.4 2.691 1 0.1009summary(g03$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4553.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9839 -0.5287 0.1117 0.6716 2.6967
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.077961 0.27921
## Xr.0 s(visitNum_centered):trt2Weighted first 0.397553 0.63052
## Xr s(visitNum_centered):trt2Sham first 0.005922 0.07696
## Residual 0.384011 0.61969
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 3.58211 0.05438 65.87
## XtreatmentWeighted -0.32459 0.04854 -6.69
## Xs(visitNum_centered):trt2Sham firstFx1 0.06166 0.03320 1.86
## Xs(visitNum_centered):trt2Weighted firstFx1 0.01321 0.19301 0.07
##
## Correlation of Fixed Effects:
## X(Int) XtrtmW X(N_):2Sf
## XtrtmntWght -0.451
## X(N_):2SfF1 0.228 -0.510
## X(N_):2WfF1 0.040 0.017 -0.009g04 <- gamm4(log(amp_acc) ~ s(visitNum_centered) + treatment, random = ~(1|beeID), data = newdf3)
anova(g03$mer, g04$mer) #g04 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g04$mer: NULL
## g03$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g04$mer 6 4551.2 4585.8 -2269.6 4539.2
## g03$mer 8 4553.1 4599.2 -2268.5 4537.1 2.1425 2 0.3426summary(g04$gam) # approx p-value for smooth##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(amp_acc) ~ s(visitNum_centered) + treatment
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.56539 0.05047 70.64 <2e-16 ***
## treatmentWeighted -0.29794 0.02688 -11.08 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered) 2.056 2.056 6.862 0.00106 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0378
## lmer.REML = 4555.5 Scale est. = 0.38524 n = 2360summary(g04$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4555.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0433 -0.5427 0.1059 0.6832 2.7605
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07754 0.2785
## Xr s(visitNum_centered) 0.02027 0.1424
## Residual 0.38524 0.6207
## Number of obs: 2360, groups: beeID, 36; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 3.56539 0.05047 70.64
## XtreatmentWeighted -0.29794 0.02688 -11.08
## Xs(visitNum_centered)Fx1 0.02517 0.04290 0.59
##
## Correlation of Fixed Effects:
## X(Int) XtrtmW
## XtrtmntWght -0.293
## Xs(vstN_)F1 0.024 -0.053g44 <- gamm4(log(amp_acc) ~ visitNum_centered + treatment, random = ~(1|beeID), data = newdf3)
g05 <- gamm4(log(amp_acc) ~ treatment, random = ~(1|beeID), data = newdf3)
anova(g44$mer, g05$mer) #g44 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g05$mer: NULL
## g44$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g05$mer 4 4560.8 4583.9 -2276.4 4552.8
## g44$mer 5 4549.2 4578.0 -2269.6 4539.2 13.63 1 0.0002226 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1g06 <- gamm4(log(amp_acc) ~ visitNum_centered , random = ~(1|beeID), data = newdf3)
anova(g44$mer, g06$mer) #g044 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g06$mer: NULL
## g44$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g06$mer 4 4666.2 4689.3 -2329.1 4658.2
## g44$mer 5 4549.2 4578.0 -2269.6 4539.2 119.02 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# final model -- only treatment matters
ampMod <- g04
summary(ampMod$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4555.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0433 -0.5427 0.1059 0.6832 2.7605
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07754 0.2785
## Xr s(visitNum_centered) 0.02027 0.1424
## Residual 0.38524 0.6207
## Number of obs: 2360, groups: beeID, 36; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 3.56539 0.05047 70.64
## XtreatmentWeighted -0.29794 0.02688 -11.08
## Xs(visitNum_centered)Fx1 0.02517 0.04290 0.59
##
## Correlation of Fixed Effects:
## X(Int) XtrtmW
## XtrtmntWght -0.293
## Xs(vstN_)F1 0.024 -0.053summary(ampMod$gam)##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(amp_acc) ~ s(visitNum_centered) + treatment
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.56539 0.05047 70.64 <2e-16 ***
## treatmentWeighted -0.29794 0.02688 -11.08 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered) 2.056 2.056 6.862 0.00106 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0378
## lmer.REML = 4555.5 Scale est. = 0.38524 n = 2360plot(ampMod$mer)
par(mfrow = c(2,1))
plot(ampMod$gam, all.terms = TRUE, rug = FALSE, shade = TRUE)
dev.off()## null device
## 1Modeling amplitude with lmer
# log transform for acceleration helps model fit better
# start with large model (including interaction)
ma0 = lmer(log(amp_acc) ~ visitNum_centered*trt2 + hive +IT * treatment+ (1|beeID), data = newdf3, REML = FALSE)
summary(ma0)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## log(amp_acc) ~ visitNum_centered * trt2 + hive + IT * treatment +
## (1 | beeID)
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4541.7 4599.3 -2260.8 4521.7 2350
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0318 -0.5397 0.1116 0.6862 2.6657
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.06647 0.2578
## Residual 0.38294 0.6188
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.3181167 0.5736148 5.785
## visitNum_centered 0.0017926 0.0010587 1.693
## trt2Weighted first -0.0608425 0.0918382 -0.662
## hive4 0.0948197 0.0975308 0.972
## IT 0.0589548 0.1420758 0.415
## treatmentWeighted -1.4174293 0.3083754 -4.596
## visitNum_centered:trt2Weighted first -0.0004062 0.0020914 -0.194
## IT:treatmentWeighted 0.2808255 0.0780233 3.599
##
## Correlation of Fixed Effects:
## (Intr) vstNm_ trt2Wf hive4 IT trtmnW vN_:2f
## vstNm_cntrd -0.015
## trt2Wghtdfr -0.229 0.040
## hive4 -0.038 -0.014 -0.013
## IT -0.992 0.038 0.162 -0.014
## trtmntWghtd -0.312 0.142 0.014 -0.009 0.316
## vstNm_c:2Wf -0.022 -0.805 -0.027 0.005 -0.005 -0.002
## IT:trtmntWg 0.307 -0.241 -0.016 0.010 -0.317 -0.990 0.115ma1 = update(ma0, .~. - visitNum_centered:trt2)
BIC(ma0, ma1) # interaction, ma1, is better## df BIC
## ma0 10 4599.347
## ma1 9 4591.618# pval for interaction (in case paper needs it)
anova(ma0, ma1)## Data: newdf3
## Models:
## ma1: log(amp_acc) ~ visitNum_centered + trt2 + hive + IT + treatment +
## ma1: (1 | beeID) + IT:treatment
## ma0: log(amp_acc) ~ visitNum_centered * trt2 + hive + IT * treatment +
## ma0: (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma1 9 4539.7 4591.6 -2260.9 4521.7
## ma0 10 4541.7 4599.3 -2260.8 4521.7 0.0377 1 0.846summary(ma1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## log(amp_acc) ~ visitNum_centered + trt2 + hive + IT + treatment +
## (1 | beeID) + IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4539.7 4591.6 -2260.9 4521.7 2351
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0255 -0.5401 0.1127 0.6850 2.6689
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.06652 0.2579
## Residual 0.38294 0.6188
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.3156701 0.5736617 5.780
## visitNum_centered 0.0016270 0.0006282 2.590
## trt2Weighted first -0.0613216 0.0918373 -0.668
## hive4 0.0949225 0.0975640 0.973
## IT 0.0588142 0.1421196 0.414
## treatmentWeighted -1.4175699 0.3083761 -4.597
## IT:treatmentWeighted 0.2825651 0.0775090 3.646
##
## Correlation of Fixed Effects:
## (Intr) vstNm_ trt2Wf hive4 IT trtmnW
## vstNm_cntrd -0.055
## trt2Wghtdfr -0.229 0.031
## hive4 -0.038 -0.016 -0.013
## IT -0.993 0.056 0.162 -0.014
## trtmntWghtd -0.312 0.236 0.014 -0.009 0.316
## IT:trtmntWg 0.312 -0.253 -0.013 0.009 -0.318 -0.996ma2 <- update(ma1, .~. - trt2)
BIC(ma1, ma2) # keep ma2## df BIC
## ma1 9 4591.618
## ma2 8 4584.295summary(ma2)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: log(amp_acc) ~ visitNum_centered + hive + IT + treatment + (1 |
## beeID) + IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4538.2 4584.3 -2261.1 4522.2 2352
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0293 -0.5416 0.1160 0.6854 2.6651
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.06752 0.2598
## Residual 0.38294 0.6188
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.227873 0.561839 5.745
## visitNum_centered 0.001640 0.000628 2.611
## hive4 0.094133 0.098224 0.958
## IT 0.074144 0.141118 0.525
## treatmentWeighted -1.414972 0.308358 -4.589
## IT:treatmentWeighted 0.281940 0.077505 3.638
##
## Correlation of Fixed Effects:
## (Intr) vstNm_ hive4 IT trtmnW
## vstNm_cntrd -0.049
## hive4 -0.042 -0.016
## IT -0.995 0.052 -0.012
## trtmntWghtd -0.315 0.235 -0.008 0.316
## IT:trtmntWg 0.316 -0.252 0.009 -0.318 -0.996ma3 <- update(ma2, .~. - hive)
anova(ma2, ma3) # keep ma3## Data: newdf3
## Models:
## ma3: log(amp_acc) ~ visitNum_centered + IT + treatment + (1 | beeID) +
## ma3: IT:treatment
## ma2: log(amp_acc) ~ visitNum_centered + hive + IT + treatment + (1 |
## ma2: beeID) + IT:treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma3 7 4537.1 4577.4 -2261.5 4523.1
## ma2 8 4538.2 4584.3 -2261.1 4522.2 0.9083 1 0.3406summary(ma3)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## log(amp_acc) ~ visitNum_centered + IT + treatment + (1 | beeID) +
## IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4537.1 4577.4 -2261.5 4523.1 2353
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0319 -0.5419 0.1149 0.6887 2.6771
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.06929 0.2632
## Residual 0.38295 0.6188
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.250421 0.567438 5.728
## visitNum_centered 0.001648 0.000628 2.625
## IT 0.075722 0.142637 0.531
## treatmentWeighted -1.412882 0.308373 -4.582
## IT:treatmentWeighted 0.281383 0.077509 3.630
##
## Correlation of Fixed Effects:
## (Intr) vstNm_ IT trtmnW
## vstNm_cntrd -0.049
## IT -0.996 0.051
## trtmntWghtd -0.312 0.235 0.312
## IT:trtmntWg 0.313 -0.252 -0.315 -0.996ma3.1 <- update(ma3, .~. - visitNum_centered)
anova(ma3, ma3.1) # keep 3.1## Data: newdf3
## Models:
## ma3.1: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## ma3: log(amp_acc) ~ visitNum_centered + IT + treatment + (1 | beeID) +
## ma3: IT:treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma3.1 6 4541.9 4576.5 -2265.0 4529.9
## ma3 7 4537.1 4577.4 -2261.5 4523.1 6.877 1 0.008731 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(ma3.1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4541.9 4576.5 -2265.0 4529.9 2354
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0202 -0.5393 0.1093 0.6834 2.6666
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07006 0.2647
## Residual 0.38402 0.6197
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.32371 0.56952 5.836
## IT 0.05660 0.14315 0.395
## treatmentWeighted -1.60343 0.30014 -5.342
## IT:treatmentWeighted 0.33276 0.07511 4.431
##
## Correlation of Fixed Effects:
## (Intr) IT trtmnW
## IT -0.996
## trtmntWghtd -0.309 0.308
## IT:trtmntWg 0.310 -0.312 -0.996ma4 <- update(ma3.1, .~. - visitNum_centered )
anova(ma3.1, ma4) #keep ma3.1## Data: newdf3
## Models:
## ma3.1: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## ma4: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma3.1 6 4541.9 4576.5 -2265 4529.9
## ma4 6 4541.9 4576.5 -2265 4529.9 0 0 1summary(ma3.1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4541.9 4576.5 -2265.0 4529.9 2354
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0202 -0.5393 0.1093 0.6834 2.6666
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07006 0.2647
## Residual 0.38402 0.6197
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.32371 0.56952 5.836
## IT 0.05660 0.14315 0.395
## treatmentWeighted -1.60343 0.30014 -5.342
## IT:treatmentWeighted 0.33276 0.07511 4.431
##
## Correlation of Fixed Effects:
## (Intr) IT trtmnW
## IT -0.996
## trtmntWghtd -0.309 0.308
## IT:trtmntWg 0.310 -0.312 -0.996m3.2 <- update(ma3.1, .~ . + I(scale(visitNum_centered)) + I(scale(visitNum_centered^2)) + (1|beeID))
summary(m3.2)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## log(amp_acc) ~ IT + treatment + (1 | beeID) + I(scale(visitNum_centered)) +
## I(scale(visitNum_centered^2)) + IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4539.1 4585.2 -2261.5 4523.1 2352
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0308 -0.5413 0.1154 0.6887 2.6758
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.06929 0.2632
## Residual 0.38294 0.6188
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.26035 0.56770 5.743
## IT 0.07536 0.14273 0.528
## treatmentWeighted -1.41125 0.30921 -4.564
## I(scale(visitNum_centered)) 0.03784 0.01705 2.219
## I(scale(visitNum_centered^2)) 0.00129 0.01797 0.072
## IT:treatmentWeighted 0.28096 0.07774 3.614
##
## Correlation of Fixed Effects:
## (Intr) IT trtmnW I((N_) I((N_^
## IT -0.996
## trtmntWghtd -0.307 0.309
## I(scl(vN_)) -0.057 0.062 0.164
## I(sc(N_^2)) 0.038 -0.035 0.074 -0.511
## IT:trtmntWg 0.308 -0.311 -0.996 -0.177 -0.076anova(ma3.1, m3.2) # keep ma3.1 (according to BIC)## Data: newdf3
## Models:
## ma3.1: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## m3.2: log(amp_acc) ~ IT + treatment + (1 | beeID) + I(scale(visitNum_centered)) +
## m3.2: I(scale(visitNum_centered^2)) + IT:treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma3.1 6 4541.9 4576.5 -2265.0 4529.9
## m3.2 8 4539.1 4585.2 -2261.5 4523.1 6.8821 2 0.03203 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1finmod <- update(ma3.1, .~., REML = TRUE)
summary(finmod)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## Data: newdf3
##
## REML criterion at convergence: 4545.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0179 -0.5395 0.1071 0.6826 2.6697
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07463 0.2732
## Residual 0.38434 0.6200
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.32401 0.58488 5.683
## IT 0.05653 0.14700 0.385
## treatmentWeighted -1.60422 0.30031 -5.342
## IT:treatmentWeighted 0.33294 0.07515 4.430
##
## Correlation of Fixed Effects:
## (Intr) IT trtmnW
## IT -0.996
## trtmntWghtd -0.301 0.300
## IT:trtmntWg 0.302 -0.303 -0.996# get p-value for interaction for paper
pvalMod <- update(ma3.1, .~. - IT:treatment)
anova(ma3.1, pvalMod)## Data: newdf3
## Models:
## pvalMod: log(amp_acc) ~ IT + treatment + (1 | beeID)
## ma3.1: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## pvalMod 5 4559.5 4588.3 -2274.8 4549.5
## ma3.1 6 4541.9 4576.5 -2265.0 4529.9 19.545 1 9.826e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# diagnostics
plot(finmod)
qqnorm(ranef(finmod)$beeID[[1]])
qqline(ranef(finmod)$beeID[[1]])
sjp.lmer(finmod) # plot random effects to find any outliers## Plotting random effects...
sjp.lmer(finmod, type = 'fe', sort = TRUE, p.kr = FALSE) # plot fixed effects## Computing p-values via Wald-statistics approximation (treating t as Wald z).
Bootstrap CI’s for amplitude for figure for paper
# set number of bootstrap replicates for models
nbootSims2 = 10000
# using hive 3, since it's the one with the most data
pframe <- expand.grid(trt2 = levels(droplevels(newdf3$trt2)),
IT = c(ITmean, seq(min(newdf3$IT), max(newdf3$IT), length.out = 50)),
visitNum_centered = -50:50,
hive = factor(3, levels = levels(newdf3$hive)),
beeID = 99999,
treatment = levels(droplevels(newdf3$treatment)))
pframe$amp_acc <- 0
pframe2 <- pframe[(pframe$trt2 == "Sham first" &
pframe$treatment == "Sham" &
pframe$visitNum_centered < 0) |
(pframe$trt2 == "Sham first" &
pframe$treatment == "Weighted" &
pframe$visitNum_centered > 0) |
(pframe$trt2 == "Weighted first" &
pframe$treatment == "Weighted" &
pframe$visitNum_centered < 0) |
(pframe$trt2 == "Weighted first" &
pframe$treatment == "Sham" &
pframe$visitNum_centered > 0)
, ]
# exponentiate to put on original scale
pp <- exp(predict(finmod, newdata = pframe2, re.form=NA, type = 'response')) # re.form sets all random effects to 0
### Calculate CI's (using bootstrap, not accounting for random effects)
bb2 <- bootMer(finmod, FUN=function(x) predict(x, pframe2, re.form=NA, type = 'response'), nsim = nbootSims2)## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce q
## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce qprint(paste("Number of bootstrap samples", nrow(bb2$t)))## [1] "Number of bootstrap samples 10000"bb2_se <-apply(bb2$t,2,function(x) quantile(x, probs = c(0.025, 0.975)))
pframe2$blo<- exp(bb2_se[1,]) # exponentiate to put on original scale
pframe2$bhi<- exp(bb2_se[2,])
pframe2$predMean <- pp
pframe2## trt2 IT visitNum_centered hive beeID treatment
## 1 Sham first 3.965833 -50 3 99999 Sham
## 3 Sham first 3.120000 -50 3 99999 Sham
## 5 Sham first 3.154490 -50 3 99999 Sham
## 7 Sham first 3.188980 -50 3 99999 Sham
## 9 Sham first 3.223469 -50 3 99999 Sham
## 11 Sham first 3.257959 -50 3 99999 Sham
## 13 Sham first 3.292449 -50 3 99999 Sham
## 15 Sham first 3.326939 -50 3 99999 Sham
## 17 Sham first 3.361429 -50 3 99999 Sham
## 19 Sham first 3.395918 -50 3 99999 Sham
## 21 Sham first 3.430408 -50 3 99999 Sham
## 23 Sham first 3.464898 -50 3 99999 Sham
## 25 Sham first 3.499388 -50 3 99999 Sham
## 27 Sham first 3.533878 -50 3 99999 Sham
## 29 Sham first 3.568367 -50 3 99999 Sham
## 31 Sham first 3.602857 -50 3 99999 Sham
## 33 Sham first 3.637347 -50 3 99999 Sham
## 35 Sham first 3.671837 -50 3 99999 Sham
## 37 Sham first 3.706327 -50 3 99999 Sham
## 39 Sham first 3.740816 -50 3 99999 Sham
## 41 Sham first 3.775306 -50 3 99999 Sham
## 43 Sham first 3.809796 -50 3 99999 Sham
## 45 Sham first 3.844286 -50 3 99999 Sham
## 47 Sham first 3.878776 -50 3 99999 Sham
## 49 Sham first 3.913265 -50 3 99999 Sham
## 51 Sham first 3.947755 -50 3 99999 Sham
## 53 Sham first 3.982245 -50 3 99999 Sham
## 55 Sham first 4.016735 -50 3 99999 Sham
## 57 Sham first 4.051224 -50 3 99999 Sham
## 59 Sham first 4.085714 -50 3 99999 Sham
## 61 Sham first 4.120204 -50 3 99999 Sham
## 63 Sham first 4.154694 -50 3 99999 Sham
## 65 Sham first 4.189184 -50 3 99999 Sham
## 67 Sham first 4.223673 -50 3 99999 Sham
## 69 Sham first 4.258163 -50 3 99999 Sham
## 71 Sham first 4.292653 -50 3 99999 Sham
## 73 Sham first 4.327143 -50 3 99999 Sham
## 75 Sham first 4.361633 -50 3 99999 Sham
## 77 Sham first 4.396122 -50 3 99999 Sham
## 79 Sham first 4.430612 -50 3 99999 Sham
## 81 Sham first 4.465102 -50 3 99999 Sham
## 83 Sham first 4.499592 -50 3 99999 Sham
## 85 Sham first 4.534082 -50 3 99999 Sham
## 87 Sham first 4.568571 -50 3 99999 Sham
## 89 Sham first 4.603061 -50 3 99999 Sham
## 91 Sham first 4.637551 -50 3 99999 Sham
## 93 Sham first 4.672041 -50 3 99999 Sham
## 95 Sham first 4.706531 -50 3 99999 Sham
## 97 Sham first 4.741020 -50 3 99999 Sham
## 99 Sham first 4.775510 -50 3 99999 Sham
## 101 Sham first 4.810000 -50 3 99999 Sham
## 103 Sham first 3.965833 -49 3 99999 Sham
## 105 Sham first 3.120000 -49 3 99999 Sham
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## 1995 Sham first 4.051224 -31 3 99999 Sham
## 1997 Sham first 4.085714 -31 3 99999 Sham
## 1999 Sham first 4.120204 -31 3 99999 Sham
## 2001 Sham first 4.154694 -31 3 99999 Sham
## 2003 Sham first 4.189184 -31 3 99999 Sham
## 2005 Sham first 4.223673 -31 3 99999 Sham
## 2007 Sham first 4.258163 -31 3 99999 Sham
## 2009 Sham first 4.292653 -31 3 99999 Sham
## 2011 Sham first 4.327143 -31 3 99999 Sham
## 2013 Sham first 4.361633 -31 3 99999 Sham
## 2015 Sham first 4.396122 -31 3 99999 Sham
## 2017 Sham first 4.430612 -31 3 99999 Sham
## 2019 Sham first 4.465102 -31 3 99999 Sham
## 2021 Sham first 4.499592 -31 3 99999 Sham
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## 20177 Sham first 4.499592 46 3 99999 Weighted
## 20179 Sham first 4.534082 46 3 99999 Weighted
## 20181 Sham first 4.568571 46 3 99999 Weighted
## 20183 Sham first 4.603061 46 3 99999 Weighted
## 20185 Sham first 4.637551 46 3 99999 Weighted
## 20187 Sham first 4.672041 46 3 99999 Weighted
## 20189 Sham first 4.706531 46 3 99999 Weighted
## 20191 Sham first 4.741020 46 3 99999 Weighted
## 20193 Sham first 4.775510 46 3 99999 Weighted
## 20195 Sham first 4.810000 46 3 99999 Weighted
## 20197 Sham first 3.965833 47 3 99999 Weighted
## 20199 Sham first 3.120000 47 3 99999 Weighted
## 20201 Sham first 3.154490 47 3 99999 Weighted
## amp_acc blo bhi predMean
## 1 0 31.57351 38.22125 34.75029
## 3 0 25.49506 42.84594 33.12789
## 5 0 25.79680 42.54551 33.19254
## 7 0 26.08927 42.24944 33.25732
## 9 0 26.40829 41.93358 33.32222
## 11 0 26.72064 41.64990 33.38725
## 13 0 27.01942 41.39490 33.45240
## 15 0 27.31751 41.11298 33.51768
## 17 0 27.61339 40.82644 33.58309
## 19 0 27.90661 40.54014 33.64863
## 21 0 28.19609 40.27338 33.71430
## 23 0 28.49678 40.06086 33.78009
## 25 0 28.78249 39.84688 33.84601
## 27 0 29.06993 39.63330 33.91206
## 29 0 29.34846 39.42863 33.97824
## 31 0 29.60349 39.19437 34.04455
## 33 0 29.87907 38.97263 34.11099
## 35 0 30.13658 38.77901 34.17755
## 37 0 30.37774 38.59949 34.24425
## 39 0 30.60230 38.46750 34.31108
## 41 0 30.83041 38.29356 34.37804
## 43 0 31.02157 38.23188 34.44513
## 45 0 31.18995 38.15239 34.51235
## 47 0 31.33233 38.14010 34.57970
## 49 0 31.45404 38.13786 34.64718
## 51 0 31.54964 38.17331 34.71479
## 53 0 31.60184 38.27274 34.78254
## 55 0 31.61696 38.39085 34.85042
## 57 0 31.62603 38.52794 34.91843
## 59 0 31.56865 38.73447 34.98657
## 61 0 31.51867 38.97780 35.05485
## 63 0 31.44552 39.20849 35.12326
## 65 0 31.33122 39.51717 35.19180
## 67 0 31.19991 39.83389 35.26048
## 69 0 31.03491 40.16235 35.32929
## 71 0 30.89209 40.46851 35.39823
## 73 0 30.71310 40.82804 35.46731
## 75 0 30.54784 41.23575 35.53652
## 77 0 30.35885 41.61929 35.60587
## 79 0 30.15304 42.04120 35.67536
## 81 0 29.95922 42.50007 35.74498
## 83 0 29.74378 42.95225 35.81474
## 85 0 29.54147 43.44571 35.88463
## 87 0 29.34086 43.86883 35.95466
## 89 0 29.11854 44.35254 36.02482
## 91 0 28.91356 44.82052 36.09512
## 93 0 28.70973 45.38433 36.16556
## 95 0 28.52517 45.88702 36.23614
## 97 0 28.33535 46.39912 36.30686
## 99 0 28.15172 46.92695 36.37771
## 101 0 27.96350 47.43410 36.44870
## 103 0 31.57351 38.22125 34.75029
## 105 0 25.49506 42.84594 33.12789
## 107 0 25.79680 42.54551 33.19254
## 109 0 26.08927 42.24944 33.25732
## 111 0 26.40829 41.93358 33.32222
## 113 0 26.72064 41.64990 33.38725
## 115 0 27.01942 41.39490 33.45240
## 117 0 27.31751 41.11298 33.51768
## 119 0 27.61339 40.82644 33.58309
## 121 0 27.90661 40.54014 33.64863
## 123 0 28.19609 40.27338 33.71430
## 125 0 28.49678 40.06086 33.78009
## 127 0 28.78249 39.84688 33.84601
## 129 0 29.06993 39.63330 33.91206
## 131 0 29.34846 39.42863 33.97824
## 133 0 29.60349 39.19437 34.04455
## 135 0 29.87907 38.97263 34.11099
## 137 0 30.13658 38.77901 34.17755
## 139 0 30.37774 38.59949 34.24425
## 141 0 30.60230 38.46750 34.31108
## 143 0 30.83041 38.29356 34.37804
## 145 0 31.02157 38.23188 34.44513
## 147 0 31.18995 38.15239 34.51235
## 149 0 31.33233 38.14010 34.57970
## 151 0 31.45404 38.13786 34.64718
## 153 0 31.54964 38.17331 34.71479
## 155 0 31.60184 38.27274 34.78254
## 157 0 31.61696 38.39085 34.85042
## 159 0 31.62603 38.52794 34.91843
## 161 0 31.56865 38.73447 34.98657
## 163 0 31.51867 38.97780 35.05485
## 165 0 31.44552 39.20849 35.12326
## 167 0 31.33122 39.51717 35.19180
## 169 0 31.19991 39.83389 35.26048
## 171 0 31.03491 40.16235 35.32929
## 173 0 30.89209 40.46851 35.39823
## 175 0 30.71310 40.82804 35.46731
## 177 0 30.54784 41.23575 35.53652
## 179 0 30.35885 41.61929 35.60587
## 181 0 30.15304 42.04120 35.67536
## 183 0 29.95922 42.50007 35.74498
## 185 0 29.74378 42.95225 35.81474
## 187 0 29.54147 43.44571 35.88463
## 189 0 29.34086 43.86883 35.95466
## 191 0 29.11854 44.35254 36.02482
## 193 0 28.91356 44.82052 36.09512
## 195 0 28.70973 45.38433 36.16556
## 197 0 28.52517 45.88702 36.23614
## 199 0 28.33535 46.39912 36.30686
## 201 0 28.15172 46.92695 36.37771
## 203 0 27.96350 47.43410 36.44870
## 205 0 31.57351 38.22125 34.75029
## 207 0 25.49506 42.84594 33.12789
## 209 0 25.79680 42.54551 33.19254
## 211 0 26.08927 42.24944 33.25732
## 213 0 26.40829 41.93358 33.32222
## 215 0 26.72064 41.64990 33.38725
## 217 0 27.01942 41.39490 33.45240
## 219 0 27.31751 41.11298 33.51768
## 221 0 27.61339 40.82644 33.58309
## 223 0 27.90661 40.54014 33.64863
## 225 0 28.19609 40.27338 33.71430
## 227 0 28.49678 40.06086 33.78009
## 229 0 28.78249 39.84688 33.84601
## 231 0 29.06993 39.63330 33.91206
## 233 0 29.34846 39.42863 33.97824
## 235 0 29.60349 39.19437 34.04455
## 237 0 29.87907 38.97263 34.11099
## 239 0 30.13658 38.77901 34.17755
## 241 0 30.37774 38.59949 34.24425
## 243 0 30.60230 38.46750 34.31108
## 245 0 30.83041 38.29356 34.37804
## 247 0 31.02157 38.23188 34.44513
## 249 0 31.18995 38.15239 34.51235
## 251 0 31.33233 38.14010 34.57970
## 253 0 31.45404 38.13786 34.64718
## 255 0 31.54964 38.17331 34.71479
## 257 0 31.60184 38.27274 34.78254
## 259 0 31.61696 38.39085 34.85042
## 261 0 31.62603 38.52794 34.91843
## 263 0 31.56865 38.73447 34.98657
## 265 0 31.51867 38.97780 35.05485
## 267 0 31.44552 39.20849 35.12326
## 269 0 31.33122 39.51717 35.19180
## 271 0 31.19991 39.83389 35.26048
## 273 0 31.03491 40.16235 35.32929
## 275 0 30.89209 40.46851 35.39823
## 277 0 30.71310 40.82804 35.46731
## 279 0 30.54784 41.23575 35.53652
## 281 0 30.35885 41.61929 35.60587
## 283 0 30.15304 42.04120 35.67536
## 285 0 29.95922 42.50007 35.74498
## 287 0 29.74378 42.95225 35.81474
## 289 0 29.54147 43.44571 35.88463
## 291 0 29.34086 43.86883 35.95466
## 293 0 29.11854 44.35254 36.02482
## 295 0 28.91356 44.82052 36.09512
## 297 0 28.70973 45.38433 36.16556
## 299 0 28.52517 45.88702 36.23614
## 301 0 28.33535 46.39912 36.30686
## 303 0 28.15172 46.92695 36.37771
## 305 0 27.96350 47.43410 36.44870
## 307 0 31.57351 38.22125 34.75029
## 309 0 25.49506 42.84594 33.12789
## 311 0 25.79680 42.54551 33.19254
## 313 0 26.08927 42.24944 33.25732
## 315 0 26.40829 41.93358 33.32222
## 317 0 26.72064 41.64990 33.38725
## 319 0 27.01942 41.39490 33.45240
## 321 0 27.31751 41.11298 33.51768
## 323 0 27.61339 40.82644 33.58309
## 325 0 27.90661 40.54014 33.64863
## 327 0 28.19609 40.27338 33.71430
## 329 0 28.49678 40.06086 33.78009
## 331 0 28.78249 39.84688 33.84601
## 333 0 29.06993 39.63330 33.91206
## 335 0 29.34846 39.42863 33.97824
## 337 0 29.60349 39.19437 34.04455
## 339 0 29.87907 38.97263 34.11099
## 341 0 30.13658 38.77901 34.17755
## 343 0 30.37774 38.59949 34.24425
## 345 0 30.60230 38.46750 34.31108
## 347 0 30.83041 38.29356 34.37804
## 349 0 31.02157 38.23188 34.44513
## 351 0 31.18995 38.15239 34.51235
## 353 0 31.33233 38.14010 34.57970
## 355 0 31.45404 38.13786 34.64718
## 357 0 31.54964 38.17331 34.71479
## 359 0 31.60184 38.27274 34.78254
## 361 0 31.61696 38.39085 34.85042
## 363 0 31.62603 38.52794 34.91843
## 365 0 31.56865 38.73447 34.98657
## 367 0 31.51867 38.97780 35.05485
## 369 0 31.44552 39.20849 35.12326
## 371 0 31.33122 39.51717 35.19180
## 373 0 31.19991 39.83389 35.26048
## 375 0 31.03491 40.16235 35.32929
## 377 0 30.89209 40.46851 35.39823
## 379 0 30.71310 40.82804 35.46731
## 381 0 30.54784 41.23575 35.53652
## 383 0 30.35885 41.61929 35.60587
## 385 0 30.15304 42.04120 35.67536
## 387 0 29.95922 42.50007 35.74498
## 389 0 29.74378 42.95225 35.81474
## 391 0 29.54147 43.44571 35.88463
## 393 0 29.34086 43.86883 35.95466
## 395 0 29.11854 44.35254 36.02482
## 397 0 28.91356 44.82052 36.09512
## 399 0 28.70973 45.38433 36.16556
## 401 0 28.52517 45.88702 36.23614
## 403 0 28.33535 46.39912 36.30686
## 405 0 28.15172 46.92695 36.37771
## 407 0 27.96350 47.43410 36.44870
## 409 0 31.57351 38.22125 34.75029
## 411 0 25.49506 42.84594 33.12789
## 413 0 25.79680 42.54551 33.19254
## 415 0 26.08927 42.24944 33.25732
## 417 0 26.40829 41.93358 33.32222
## 419 0 26.72064 41.64990 33.38725
## 421 0 27.01942 41.39490 33.45240
## 423 0 27.31751 41.11298 33.51768
## 425 0 27.61339 40.82644 33.58309
## 427 0 27.90661 40.54014 33.64863
## 429 0 28.19609 40.27338 33.71430
## 431 0 28.49678 40.06086 33.78009
## 433 0 28.78249 39.84688 33.84601
## 435 0 29.06993 39.63330 33.91206
## 437 0 29.34846 39.42863 33.97824
## 439 0 29.60349 39.19437 34.04455
## 441 0 29.87907 38.97263 34.11099
## 443 0 30.13658 38.77901 34.17755
## 445 0 30.37774 38.59949 34.24425
## 447 0 30.60230 38.46750 34.31108
## 449 0 30.83041 38.29356 34.37804
## 451 0 31.02157 38.23188 34.44513
## 453 0 31.18995 38.15239 34.51235
## 455 0 31.33233 38.14010 34.57970
## 457 0 31.45404 38.13786 34.64718
## 459 0 31.54964 38.17331 34.71479
## 461 0 31.60184 38.27274 34.78254
## 463 0 31.61696 38.39085 34.85042
## 465 0 31.62603 38.52794 34.91843
## 467 0 31.56865 38.73447 34.98657
## 469 0 31.51867 38.97780 35.05485
## 471 0 31.44552 39.20849 35.12326
## 473 0 31.33122 39.51717 35.19180
## 475 0 31.19991 39.83389 35.26048
## 477 0 31.03491 40.16235 35.32929
## 479 0 30.89209 40.46851 35.39823
## 481 0 30.71310 40.82804 35.46731
## 483 0 30.54784 41.23575 35.53652
## 485 0 30.35885 41.61929 35.60587
## 487 0 30.15304 42.04120 35.67536
## 489 0 29.95922 42.50007 35.74498
## 491 0 29.74378 42.95225 35.81474
## 493 0 29.54147 43.44571 35.88463
## 495 0 29.34086 43.86883 35.95466
## 497 0 29.11854 44.35254 36.02482
## 499 0 28.91356 44.82052 36.09512
## 501 0 28.70973 45.38433 36.16556
## 503 0 28.52517 45.88702 36.23614
## 505 0 28.33535 46.39912 36.30686
## 507 0 28.15172 46.92695 36.37771
## 509 0 27.96350 47.43410 36.44870
## 511 0 31.57351 38.22125 34.75029
## 513 0 25.49506 42.84594 33.12789
## 515 0 25.79680 42.54551 33.19254
## 517 0 26.08927 42.24944 33.25732
## 519 0 26.40829 41.93358 33.32222
## 521 0 26.72064 41.64990 33.38725
## 523 0 27.01942 41.39490 33.45240
## 525 0 27.31751 41.11298 33.51768
## 527 0 27.61339 40.82644 33.58309
## 529 0 27.90661 40.54014 33.64863
## 531 0 28.19609 40.27338 33.71430
## 533 0 28.49678 40.06086 33.78009
## 535 0 28.78249 39.84688 33.84601
## 537 0 29.06993 39.63330 33.91206
## 539 0 29.34846 39.42863 33.97824
## 541 0 29.60349 39.19437 34.04455
## 543 0 29.87907 38.97263 34.11099
## 545 0 30.13658 38.77901 34.17755
## 547 0 30.37774 38.59949 34.24425
## 549 0 30.60230 38.46750 34.31108
## 551 0 30.83041 38.29356 34.37804
## 553 0 31.02157 38.23188 34.44513
## 555 0 31.18995 38.15239 34.51235
## 557 0 31.33233 38.14010 34.57970
## 559 0 31.45404 38.13786 34.64718
## 561 0 31.54964 38.17331 34.71479
## 563 0 31.60184 38.27274 34.78254
## 565 0 31.61696 38.39085 34.85042
## 567 0 31.62603 38.52794 34.91843
## 569 0 31.56865 38.73447 34.98657
## 571 0 31.51867 38.97780 35.05485
## 573 0 31.44552 39.20849 35.12326
## 575 0 31.33122 39.51717 35.19180
## 577 0 31.19991 39.83389 35.26048
## 579 0 31.03491 40.16235 35.32929
## 581 0 30.89209 40.46851 35.39823
## 583 0 30.71310 40.82804 35.46731
## 585 0 30.54784 41.23575 35.53652
## 587 0 30.35885 41.61929 35.60587
## 589 0 30.15304 42.04120 35.67536
## 591 0 29.95922 42.50007 35.74498
## 593 0 29.74378 42.95225 35.81474
## 595 0 29.54147 43.44571 35.88463
## 597 0 29.34086 43.86883 35.95466
## 599 0 29.11854 44.35254 36.02482
## 601 0 28.91356 44.82052 36.09512
## 603 0 28.70973 45.38433 36.16556
## 605 0 28.52517 45.88702 36.23614
## 607 0 28.33535 46.39912 36.30686
## 609 0 28.15172 46.92695 36.37771
## 611 0 27.96350 47.43410 36.44870
## 613 0 31.57351 38.22125 34.75029
## 615 0 25.49506 42.84594 33.12789
## 617 0 25.79680 42.54551 33.19254
## 619 0 26.08927 42.24944 33.25732
## 621 0 26.40829 41.93358 33.32222
## 623 0 26.72064 41.64990 33.38725
## 625 0 27.01942 41.39490 33.45240
## 627 0 27.31751 41.11298 33.51768
## 629 0 27.61339 40.82644 33.58309
## 631 0 27.90661 40.54014 33.64863
## 633 0 28.19609 40.27338 33.71430
## 635 0 28.49678 40.06086 33.78009
## 637 0 28.78249 39.84688 33.84601
## 639 0 29.06993 39.63330 33.91206
## 641 0 29.34846 39.42863 33.97824
## 643 0 29.60349 39.19437 34.04455
## 645 0 29.87907 38.97263 34.11099
## 647 0 30.13658 38.77901 34.17755
## 649 0 30.37774 38.59949 34.24425
## 651 0 30.60230 38.46750 34.31108
## 653 0 30.83041 38.29356 34.37804
## 655 0 31.02157 38.23188 34.44513
## 657 0 31.18995 38.15239 34.51235
## 659 0 31.33233 38.14010 34.57970
## 661 0 31.45404 38.13786 34.64718
## 663 0 31.54964 38.17331 34.71479
## 665 0 31.60184 38.27274 34.78254
## 667 0 31.61696 38.39085 34.85042
## 669 0 31.62603 38.52794 34.91843
## 671 0 31.56865 38.73447 34.98657
## 673 0 31.51867 38.97780 35.05485
## 675 0 31.44552 39.20849 35.12326
## 677 0 31.33122 39.51717 35.19180
## 679 0 31.19991 39.83389 35.26048
## 681 0 31.03491 40.16235 35.32929
## 683 0 30.89209 40.46851 35.39823
## 685 0 30.71310 40.82804 35.46731
## 687 0 30.54784 41.23575 35.53652
## 689 0 30.35885 41.61929 35.60587
## 691 0 30.15304 42.04120 35.67536
## 693 0 29.95922 42.50007 35.74498
## 695 0 29.74378 42.95225 35.81474
## 697 0 29.54147 43.44571 35.88463
## 699 0 29.34086 43.86883 35.95466
## 701 0 29.11854 44.35254 36.02482
## 703 0 28.91356 44.82052 36.09512
## 705 0 28.70973 45.38433 36.16556
## 707 0 28.52517 45.88702 36.23614
## 709 0 28.33535 46.39912 36.30686
## 711 0 28.15172 46.92695 36.37771
## 713 0 27.96350 47.43410 36.44870
## 715 0 31.57351 38.22125 34.75029
## 717 0 25.49506 42.84594 33.12789
## 719 0 25.79680 42.54551 33.19254
## 721 0 26.08927 42.24944 33.25732
## 723 0 26.40829 41.93358 33.32222
## 725 0 26.72064 41.64990 33.38725
## 727 0 27.01942 41.39490 33.45240
## 729 0 27.31751 41.11298 33.51768
## 731 0 27.61339 40.82644 33.58309
## 733 0 27.90661 40.54014 33.64863
## 735 0 28.19609 40.27338 33.71430
## 737 0 28.49678 40.06086 33.78009
## 739 0 28.78249 39.84688 33.84601
## 741 0 29.06993 39.63330 33.91206
## 743 0 29.34846 39.42863 33.97824
## 745 0 29.60349 39.19437 34.04455
## 747 0 29.87907 38.97263 34.11099
## 749 0 30.13658 38.77901 34.17755
## 751 0 30.37774 38.59949 34.24425
## 753 0 30.60230 38.46750 34.31108
## 755 0 30.83041 38.29356 34.37804
## 757 0 31.02157 38.23188 34.44513
## 759 0 31.18995 38.15239 34.51235
## 761 0 31.33233 38.14010 34.57970
## 763 0 31.45404 38.13786 34.64718
## 765 0 31.54964 38.17331 34.71479
## 767 0 31.60184 38.27274 34.78254
## 769 0 31.61696 38.39085 34.85042
## 771 0 31.62603 38.52794 34.91843
## 773 0 31.56865 38.73447 34.98657
## 775 0 31.51867 38.97780 35.05485
## 777 0 31.44552 39.20849 35.12326
## 779 0 31.33122 39.51717 35.19180
## 781 0 31.19991 39.83389 35.26048
## 783 0 31.03491 40.16235 35.32929
## 785 0 30.89209 40.46851 35.39823
## 787 0 30.71310 40.82804 35.46731
## 789 0 30.54784 41.23575 35.53652
## 791 0 30.35885 41.61929 35.60587
## 793 0 30.15304 42.04120 35.67536
## 795 0 29.95922 42.50007 35.74498
## 797 0 29.74378 42.95225 35.81474
## 799 0 29.54147 43.44571 35.88463
## 801 0 29.34086 43.86883 35.95466
## 803 0 29.11854 44.35254 36.02482
## 805 0 28.91356 44.82052 36.09512
## 807 0 28.70973 45.38433 36.16556
## 809 0 28.52517 45.88702 36.23614
## 811 0 28.33535 46.39912 36.30686
## 813 0 28.15172 46.92695 36.37771
## 815 0 27.96350 47.43410 36.44870
## 817 0 31.57351 38.22125 34.75029
## 819 0 25.49506 42.84594 33.12789
## 821 0 25.79680 42.54551 33.19254
## 823 0 26.08927 42.24944 33.25732
## 825 0 26.40829 41.93358 33.32222
## 827 0 26.72064 41.64990 33.38725
## 829 0 27.01942 41.39490 33.45240
## 831 0 27.31751 41.11298 33.51768
## 833 0 27.61339 40.82644 33.58309
## 835 0 27.90661 40.54014 33.64863
## 837 0 28.19609 40.27338 33.71430
## 839 0 28.49678 40.06086 33.78009
## 841 0 28.78249 39.84688 33.84601
## 843 0 29.06993 39.63330 33.91206
## 845 0 29.34846 39.42863 33.97824
## 847 0 29.60349 39.19437 34.04455
## 849 0 29.87907 38.97263 34.11099
## 851 0 30.13658 38.77901 34.17755
## 853 0 30.37774 38.59949 34.24425
## 855 0 30.60230 38.46750 34.31108
## 857 0 30.83041 38.29356 34.37804
## 859 0 31.02157 38.23188 34.44513
## 861 0 31.18995 38.15239 34.51235
## 863 0 31.33233 38.14010 34.57970
## 865 0 31.45404 38.13786 34.64718
## 867 0 31.54964 38.17331 34.71479
## 869 0 31.60184 38.27274 34.78254
## 871 0 31.61696 38.39085 34.85042
## 873 0 31.62603 38.52794 34.91843
## 875 0 31.56865 38.73447 34.98657
## 877 0 31.51867 38.97780 35.05485
## 879 0 31.44552 39.20849 35.12326
## 881 0 31.33122 39.51717 35.19180
## 883 0 31.19991 39.83389 35.26048
## 885 0 31.03491 40.16235 35.32929
## 887 0 30.89209 40.46851 35.39823
## 889 0 30.71310 40.82804 35.46731
## 891 0 30.54784 41.23575 35.53652
## 893 0 30.35885 41.61929 35.60587
## 895 0 30.15304 42.04120 35.67536
## 897 0 29.95922 42.50007 35.74498
## 899 0 29.74378 42.95225 35.81474
## 901 0 29.54147 43.44571 35.88463
## 903 0 29.34086 43.86883 35.95466
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## 1797 0 31.44552 39.20849 35.12326
## 1799 0 31.33122 39.51717 35.19180
## 1801 0 31.19991 39.83389 35.26048
## 1803 0 31.03491 40.16235 35.32929
## 1805 0 30.89209 40.46851 35.39823
## 1807 0 30.71310 40.82804 35.46731
## 1809 0 30.54784 41.23575 35.53652
## 1811 0 30.35885 41.61929 35.60587
## 1813 0 30.15304 42.04120 35.67536
## 1815 0 29.95922 42.50007 35.74498
## 1817 0 29.74378 42.95225 35.81474
## 1819 0 29.54147 43.44571 35.88463
## 1821 0 29.34086 43.86883 35.95466
## 1823 0 29.11854 44.35254 36.02482
## 1825 0 28.91356 44.82052 36.09512
## 1827 0 28.70973 45.38433 36.16556
## 1829 0 28.52517 45.88702 36.23614
## 1831 0 28.33535 46.39912 36.30686
## 1833 0 28.15172 46.92695 36.37771
## 1835 0 27.96350 47.43410 36.44870
## 1837 0 31.57351 38.22125 34.75029
## 1839 0 25.49506 42.84594 33.12789
## 1841 0 25.79680 42.54551 33.19254
## 1843 0 26.08927 42.24944 33.25732
## 1845 0 26.40829 41.93358 33.32222
## 1847 0 26.72064 41.64990 33.38725
## 1849 0 27.01942 41.39490 33.45240
## 1851 0 27.31751 41.11298 33.51768
## 1853 0 27.61339 40.82644 33.58309
## 1855 0 27.90661 40.54014 33.64863
## 1857 0 28.19609 40.27338 33.71430
## 1859 0 28.49678 40.06086 33.78009
## 1861 0 28.78249 39.84688 33.84601
## 1863 0 29.06993 39.63330 33.91206
## 1865 0 29.34846 39.42863 33.97824
## 1867 0 29.60349 39.19437 34.04455
## 1869 0 29.87907 38.97263 34.11099
## 1871 0 30.13658 38.77901 34.17755
## 1873 0 30.37774 38.59949 34.24425
## 1875 0 30.60230 38.46750 34.31108
## 1877 0 30.83041 38.29356 34.37804
## 1879 0 31.02157 38.23188 34.44513
## 1881 0 31.18995 38.15239 34.51235
## 1883 0 31.33233 38.14010 34.57970
## 1885 0 31.45404 38.13786 34.64718
## 1887 0 31.54964 38.17331 34.71479
## 1889 0 31.60184 38.27274 34.78254
## 1891 0 31.61696 38.39085 34.85042
## 1893 0 31.62603 38.52794 34.91843
## 1895 0 31.56865 38.73447 34.98657
## 1897 0 31.51867 38.97780 35.05485
## 1899 0 31.44552 39.20849 35.12326
## 1901 0 31.33122 39.51717 35.19180
## 1903 0 31.19991 39.83389 35.26048
## 1905 0 31.03491 40.16235 35.32929
## 1907 0 30.89209 40.46851 35.39823
## 1909 0 30.71310 40.82804 35.46731
## 1911 0 30.54784 41.23575 35.53652
## 1913 0 30.35885 41.61929 35.60587
## 1915 0 30.15304 42.04120 35.67536
## 1917 0 29.95922 42.50007 35.74498
## 1919 0 29.74378 42.95225 35.81474
## 1921 0 29.54147 43.44571 35.88463
## 1923 0 29.34086 43.86883 35.95466
## 1925 0 29.11854 44.35254 36.02482
## 1927 0 28.91356 44.82052 36.09512
## 1929 0 28.70973 45.38433 36.16556
## 1931 0 28.52517 45.88702 36.23614
## 1933 0 28.33535 46.39912 36.30686
## 1935 0 28.15172 46.92695 36.37771
## 1937 0 27.96350 47.43410 36.44870
## 1939 0 31.57351 38.22125 34.75029
## 1941 0 25.49506 42.84594 33.12789
## 1943 0 25.79680 42.54551 33.19254
## 1945 0 26.08927 42.24944 33.25732
## 1947 0 26.40829 41.93358 33.32222
## 1949 0 26.72064 41.64990 33.38725
## 1951 0 27.01942 41.39490 33.45240
## 1953 0 27.31751 41.11298 33.51768
## 1955 0 27.61339 40.82644 33.58309
## 1957 0 27.90661 40.54014 33.64863
## 1959 0 28.19609 40.27338 33.71430
## 1961 0 28.49678 40.06086 33.78009
## 1963 0 28.78249 39.84688 33.84601
## 1965 0 29.06993 39.63330 33.91206
## 1967 0 29.34846 39.42863 33.97824
## 1969 0 29.60349 39.19437 34.04455
## 1971 0 29.87907 38.97263 34.11099
## 1973 0 30.13658 38.77901 34.17755
## 1975 0 30.37774 38.59949 34.24425
## 1977 0 30.60230 38.46750 34.31108
## 1979 0 30.83041 38.29356 34.37804
## 1981 0 31.02157 38.23188 34.44513
## 1983 0 31.18995 38.15239 34.51235
## 1985 0 31.33233 38.14010 34.57970
## 1987 0 31.45404 38.13786 34.64718
## 1989 0 31.54964 38.17331 34.71479
## 1991 0 31.60184 38.27274 34.78254
## 1993 0 31.61696 38.39085 34.85042
## 1995 0 31.62603 38.52794 34.91843
## 1997 0 31.56865 38.73447 34.98657
## 1999 0 31.51867 38.97780 35.05485
## 2001 0 31.44552 39.20849 35.12326
## 2003 0 31.33122 39.51717 35.19180
## 2005 0 31.19991 39.83389 35.26048
## 2007 0 31.03491 40.16235 35.32929
## 2009 0 30.89209 40.46851 35.39823
## 2011 0 30.71310 40.82804 35.46731
## 2013 0 30.54784 41.23575 35.53652
## 2015 0 30.35885 41.61929 35.60587
## 2017 0 30.15304 42.04120 35.67536
## 2019 0 29.95922 42.50007 35.74498
## 2021 0 29.74378 42.95225 35.81474
## 2023 0 29.54147 43.44571 35.88463
## 2025 0 29.34086 43.86883 35.95466
## 2027 0 29.11854 44.35254 36.02482
## 2029 0 28.91356 44.82052 36.09512
## 2031 0 28.70973 45.38433 36.16556
## 2033 0 28.52517 45.88702 36.23614
## 2035 0 28.33535 46.39912 36.30686
## 2037 0 28.15172 46.92695 36.37771
## 2039 0 27.96350 47.43410 36.44870
## 2041 0 31.57351 38.22125 34.75029
## 2043 0 25.49506 42.84594 33.12789
## 2045 0 25.79680 42.54551 33.19254
## 2047 0 26.08927 42.24944 33.25732
## 2049 0 26.40829 41.93358 33.32222
## 2051 0 26.72064 41.64990 33.38725
## 2053 0 27.01942 41.39490 33.45240
## 2055 0 27.31751 41.11298 33.51768
## 2057 0 27.61339 40.82644 33.58309
## 2059 0 27.90661 40.54014 33.64863
## 2061 0 28.19609 40.27338 33.71430
## 2063 0 28.49678 40.06086 33.78009
## 2065 0 28.78249 39.84688 33.84601
## 2067 0 29.06993 39.63330 33.91206
## 2069 0 29.34846 39.42863 33.97824
## 2071 0 29.60349 39.19437 34.04455
## 2073 0 29.87907 38.97263 34.11099
## 2075 0 30.13658 38.77901 34.17755
## 2077 0 30.37774 38.59949 34.24425
## 2079 0 30.60230 38.46750 34.31108
## 2081 0 30.83041 38.29356 34.37804
## 2083 0 31.02157 38.23188 34.44513
## 2085 0 31.18995 38.15239 34.51235
## 2087 0 31.33233 38.14010 34.57970
## 2089 0 31.45404 38.13786 34.64718
## 2091 0 31.54964 38.17331 34.71479
## 2093 0 31.60184 38.27274 34.78254
## 2095 0 31.61696 38.39085 34.85042
## 2097 0 31.62603 38.52794 34.91843
## 2099 0 31.56865 38.73447 34.98657
## 2101 0 31.51867 38.97780 35.05485
## 2103 0 31.44552 39.20849 35.12326
## 2105 0 31.33122 39.51717 35.19180
## 2107 0 31.19991 39.83389 35.26048
## 2109 0 31.03491 40.16235 35.32929
## 2111 0 30.89209 40.46851 35.39823
## 2113 0 30.71310 40.82804 35.46731
## 2115 0 30.54784 41.23575 35.53652
## 2117 0 30.35885 41.61929 35.60587
## 2119 0 30.15304 42.04120 35.67536
## 2121 0 29.95922 42.50007 35.74498
## 2123 0 29.74378 42.95225 35.81474
## 2125 0 29.54147 43.44571 35.88463
## 2127 0 29.34086 43.86883 35.95466
## 2129 0 29.11854 44.35254 36.02482
## 2131 0 28.91356 44.82052 36.09512
## 2133 0 28.70973 45.38433 36.16556
## 2135 0 28.52517 45.88702 36.23614
## 2137 0 28.33535 46.39912 36.30686
## 2139 0 28.15172 46.92695 36.37771
## 2141 0 27.96350 47.43410 36.44870
## 2143 0 31.57351 38.22125 34.75029
## 2145 0 25.49506 42.84594 33.12789
## 2147 0 25.79680 42.54551 33.19254
## 2149 0 26.08927 42.24944 33.25732
## 2151 0 26.40829 41.93358 33.32222
## 2153 0 26.72064 41.64990 33.38725
## 2155 0 27.01942 41.39490 33.45240
## 2157 0 27.31751 41.11298 33.51768
## 2159 0 27.61339 40.82644 33.58309
## 2161 0 27.90661 40.54014 33.64863
## 2163 0 28.19609 40.27338 33.71430
## 2165 0 28.49678 40.06086 33.78009
## 2167 0 28.78249 39.84688 33.84601
## 2169 0 29.06993 39.63330 33.91206
## 2171 0 29.34846 39.42863 33.97824
## 2173 0 29.60349 39.19437 34.04455
## 2175 0 29.87907 38.97263 34.11099
## 2177 0 30.13658 38.77901 34.17755
## 2179 0 30.37774 38.59949 34.24425
## 2181 0 30.60230 38.46750 34.31108
## 2183 0 30.83041 38.29356 34.37804
## 2185 0 31.02157 38.23188 34.44513
## 2187 0 31.18995 38.15239 34.51235
## 2189 0 31.33233 38.14010 34.57970
## 2191 0 31.45404 38.13786 34.64718
## 2193 0 31.54964 38.17331 34.71479
## 2195 0 31.60184 38.27274 34.78254
## 2197 0 31.61696 38.39085 34.85042
## 2199 0 31.62603 38.52794 34.91843
## 2201 0 31.56865 38.73447 34.98657
## 2203 0 31.51867 38.97780 35.05485
## 2205 0 31.44552 39.20849 35.12326
## 2207 0 31.33122 39.51717 35.19180
## 2209 0 31.19991 39.83389 35.26048
## 2211 0 31.03491 40.16235 35.32929
## 2213 0 30.89209 40.46851 35.39823
## 2215 0 30.71310 40.82804 35.46731
## 2217 0 30.54784 41.23575 35.53652
## 2219 0 30.35885 41.61929 35.60587
## 2221 0 30.15304 42.04120 35.67536
## 2223 0 29.95922 42.50007 35.74498
## 2225 0 29.74378 42.95225 35.81474
## 2227 0 29.54147 43.44571 35.88463
## 2229 0 29.34086 43.86883 35.95466
## 2231 0 29.11854 44.35254 36.02482
## 2233 0 28.91356 44.82052 36.09512
## 2235 0 28.70973 45.38433 36.16556
## 2237 0 28.52517 45.88702 36.23614
## 2239 0 28.33535 46.39912 36.30686
## 2241 0 28.15172 46.92695 36.37771
## 2243 0 27.96350 47.43410 36.44870
## 2245 0 31.57351 38.22125 34.75029
## 2247 0 25.49506 42.84594 33.12789
## 2249 0 25.79680 42.54551 33.19254
## 2251 0 26.08927 42.24944 33.25732
## 2253 0 26.40829 41.93358 33.32222
## 2255 0 26.72064 41.64990 33.38725
## 2257 0 27.01942 41.39490 33.45240
## 2259 0 27.31751 41.11298 33.51768
## 2261 0 27.61339 40.82644 33.58309
## 2263 0 27.90661 40.54014 33.64863
## 2265 0 28.19609 40.27338 33.71430
## 2267 0 28.49678 40.06086 33.78009
## 2269 0 28.78249 39.84688 33.84601
## 2271 0 29.06993 39.63330 33.91206
## 2273 0 29.34846 39.42863 33.97824
## 2275 0 29.60349 39.19437 34.04455
## 2277 0 29.87907 38.97263 34.11099
## 2279 0 30.13658 38.77901 34.17755
## 2281 0 30.37774 38.59949 34.24425
## 2283 0 30.60230 38.46750 34.31108
## 2285 0 30.83041 38.29356 34.37804
## 2287 0 31.02157 38.23188 34.44513
## 2289 0 31.18995 38.15239 34.51235
## 2291 0 31.33233 38.14010 34.57970
## 2293 0 31.45404 38.13786 34.64718
## 2295 0 31.54964 38.17331 34.71479
## 2297 0 31.60184 38.27274 34.78254
## 2299 0 31.61696 38.39085 34.85042
## 2301 0 31.62603 38.52794 34.91843
## 2303 0 31.56865 38.73447 34.98657
## 2305 0 31.51867 38.97780 35.05485
## 2307 0 31.44552 39.20849 35.12326
## 2309 0 31.33122 39.51717 35.19180
## 2311 0 31.19991 39.83389 35.26048
## 2313 0 31.03491 40.16235 35.32929
## 2315 0 30.89209 40.46851 35.39823
## 2317 0 30.71310 40.82804 35.46731
## 2319 0 30.54784 41.23575 35.53652
## 2321 0 30.35885 41.61929 35.60587
## 2323 0 30.15304 42.04120 35.67536
## 2325 0 29.95922 42.50007 35.74498
## 2327 0 29.74378 42.95225 35.81474
## 2329 0 29.54147 43.44571 35.88463
## 2331 0 29.34086 43.86883 35.95466
## 2333 0 29.11854 44.35254 36.02482
## 2335 0 28.91356 44.82052 36.09512
## 2337 0 28.70973 45.38433 36.16556
## 2339 0 28.52517 45.88702 36.23614
## 2341 0 28.33535 46.39912 36.30686
## 2343 0 28.15172 46.92695 36.37771
## 2345 0 27.96350 47.43410 36.44870
## 2347 0 31.57351 38.22125 34.75029
## 2349 0 25.49506 42.84594 33.12789
## 2351 0 25.79680 42.54551 33.19254
## 2353 0 26.08927 42.24944 33.25732
## 2355 0 26.40829 41.93358 33.32222
## 2357 0 26.72064 41.64990 33.38725
## 2359 0 27.01942 41.39490 33.45240
## 2361 0 27.31751 41.11298 33.51768
## 2363 0 27.61339 40.82644 33.58309
## 2365 0 27.90661 40.54014 33.64863
## 2367 0 28.19609 40.27338 33.71430
## 2369 0 28.49678 40.06086 33.78009
## 2371 0 28.78249 39.84688 33.84601
## 2373 0 29.06993 39.63330 33.91206
## 2375 0 29.34846 39.42863 33.97824
## 2377 0 29.60349 39.19437 34.04455
## 2379 0 29.87907 38.97263 34.11099
## 2381 0 30.13658 38.77901 34.17755
## 2383 0 30.37774 38.59949 34.24425
## 2385 0 30.60230 38.46750 34.31108
## 2387 0 30.83041 38.29356 34.37804
## 2389 0 31.02157 38.23188 34.44513
## 2391 0 31.18995 38.15239 34.51235
## 2393 0 31.33233 38.14010 34.57970
## 2395 0 31.45404 38.13786 34.64718
## 2397 0 31.54964 38.17331 34.71479
## 2399 0 31.60184 38.27274 34.78254
## 2401 0 31.61696 38.39085 34.85042
## 2403 0 31.62603 38.52794 34.91843
## 2405 0 31.56865 38.73447 34.98657
## 2407 0 31.51867 38.97780 35.05485
## 2409 0 31.44552 39.20849 35.12326
## 2411 0 31.33122 39.51717 35.19180
## 2413 0 31.19991 39.83389 35.26048
## 2415 0 31.03491 40.16235 35.32929
## 2417 0 30.89209 40.46851 35.39823
## 2419 0 30.71310 40.82804 35.46731
## 2421 0 30.54784 41.23575 35.53652
## 2423 0 30.35885 41.61929 35.60587
## 2425 0 30.15304 42.04120 35.67536
## 2427 0 29.95922 42.50007 35.74498
## 2429 0 29.74378 42.95225 35.81474
## 2431 0 29.54147 43.44571 35.88463
## 2433 0 29.34086 43.86883 35.95466
## 2435 0 29.11854 44.35254 36.02482
## 2437 0 28.91356 44.82052 36.09512
## 2439 0 28.70973 45.38433 36.16556
## 2441 0 28.52517 45.88702 36.23614
## 2443 0 28.33535 46.39912 36.30686
## 2445 0 28.15172 46.92695 36.37771
## 2447 0 27.96350 47.43410 36.44870
## 2449 0 31.57351 38.22125 34.75029
## 2451 0 25.49506 42.84594 33.12789
## 2453 0 25.79680 42.54551 33.19254
## 2455 0 26.08927 42.24944 33.25732
## 2457 0 26.40829 41.93358 33.32222
## 2459 0 26.72064 41.64990 33.38725
## 2461 0 27.01942 41.39490 33.45240
## 2463 0 27.31751 41.11298 33.51768
## 2465 0 27.61339 40.82644 33.58309
## 2467 0 27.90661 40.54014 33.64863
## 2469 0 28.19609 40.27338 33.71430
## 2471 0 28.49678 40.06086 33.78009
## 2473 0 28.78249 39.84688 33.84601
## 2475 0 29.06993 39.63330 33.91206
## 2477 0 29.34846 39.42863 33.97824
## 2479 0 29.60349 39.19437 34.04455
## 2481 0 29.87907 38.97263 34.11099
## 2483 0 30.13658 38.77901 34.17755
## 2485 0 30.37774 38.59949 34.24425
## 2487 0 30.60230 38.46750 34.31108
## 2489 0 30.83041 38.29356 34.37804
## 2491 0 31.02157 38.23188 34.44513
## 2493 0 31.18995 38.15239 34.51235
## 2495 0 31.33233 38.14010 34.57970
## 2497 0 31.45404 38.13786 34.64718
## 2499 0 31.54964 38.17331 34.71479
## 2501 0 31.60184 38.27274 34.78254
## 2503 0 31.61696 38.39085 34.85042
## 2505 0 31.62603 38.52794 34.91843
## 2507 0 31.56865 38.73447 34.98657
## 2509 0 31.51867 38.97780 35.05485
## 2511 0 31.44552 39.20849 35.12326
## 2513 0 31.33122 39.51717 35.19180
## 2515 0 31.19991 39.83389 35.26048
## 2517 0 31.03491 40.16235 35.32929
## 2519 0 30.89209 40.46851 35.39823
## 2521 0 30.71310 40.82804 35.46731
## 2523 0 30.54784 41.23575 35.53652
## 2525 0 30.35885 41.61929 35.60587
## 2527 0 30.15304 42.04120 35.67536
## 2529 0 29.95922 42.50007 35.74498
## 2531 0 29.74378 42.95225 35.81474
## 2533 0 29.54147 43.44571 35.88463
## 2535 0 29.34086 43.86883 35.95466
## 2537 0 29.11854 44.35254 36.02482
## 2539 0 28.91356 44.82052 36.09512
## 2541 0 28.70973 45.38433 36.16556
## 2543 0 28.52517 45.88702 36.23614
## 2545 0 28.33535 46.39912 36.30686
## 2547 0 28.15172 46.92695 36.37771
## 2549 0 27.96350 47.43410 36.44870
## 2551 0 31.57351 38.22125 34.75029
## 2553 0 25.49506 42.84594 33.12789
## 2555 0 25.79680 42.54551 33.19254
## 2557 0 26.08927 42.24944 33.25732
## 2559 0 26.40829 41.93358 33.32222
## 2561 0 26.72064 41.64990 33.38725
## 2563 0 27.01942 41.39490 33.45240
## 2565 0 27.31751 41.11298 33.51768
## 2567 0 27.61339 40.82644 33.58309
## 2569 0 27.90661 40.54014 33.64863
## 2571 0 28.19609 40.27338 33.71430
## 2573 0 28.49678 40.06086 33.78009
## 2575 0 28.78249 39.84688 33.84601
## 2577 0 29.06993 39.63330 33.91206
## 2579 0 29.34846 39.42863 33.97824
## 2581 0 29.60349 39.19437 34.04455
## 2583 0 29.87907 38.97263 34.11099
## 2585 0 30.13658 38.77901 34.17755
## 2587 0 30.37774 38.59949 34.24425
## 2589 0 30.60230 38.46750 34.31108
## 2591 0 30.83041 38.29356 34.37804
## 2593 0 31.02157 38.23188 34.44513
## 2595 0 31.18995 38.15239 34.51235
## 2597 0 31.33233 38.14010 34.57970
## 2599 0 31.45404 38.13786 34.64718
## 2601 0 31.54964 38.17331 34.71479
## 2603 0 31.60184 38.27274 34.78254
## 2605 0 31.61696 38.39085 34.85042
## 2607 0 31.62603 38.52794 34.91843
## 2609 0 31.56865 38.73447 34.98657
## 2611 0 31.51867 38.97780 35.05485
## 2613 0 31.44552 39.20849 35.12326
## 2615 0 31.33122 39.51717 35.19180
## 2617 0 31.19991 39.83389 35.26048
## 2619 0 31.03491 40.16235 35.32929
## 2621 0 30.89209 40.46851 35.39823
## 2623 0 30.71310 40.82804 35.46731
## 2625 0 30.54784 41.23575 35.53652
## 2627 0 30.35885 41.61929 35.60587
## 2629 0 30.15304 42.04120 35.67536
## 2631 0 29.95922 42.50007 35.74498
## 2633 0 29.74378 42.95225 35.81474
## 2635 0 29.54147 43.44571 35.88463
## 2637 0 29.34086 43.86883 35.95466
## 2639 0 29.11854 44.35254 36.02482
## 2641 0 28.91356 44.82052 36.09512
## 2643 0 28.70973 45.38433 36.16556
## 2645 0 28.52517 45.88702 36.23614
## 2647 0 28.33535 46.39912 36.30686
## 2649 0 28.15172 46.92695 36.37771
## 2651 0 27.96350 47.43410 36.44870
## 2653 0 31.57351 38.22125 34.75029
## 2655 0 25.49506 42.84594 33.12789
## 2657 0 25.79680 42.54551 33.19254
## 2659 0 26.08927 42.24944 33.25732
## 2661 0 26.40829 41.93358 33.32222
## 2663 0 26.72064 41.64990 33.38725
## 2665 0 27.01942 41.39490 33.45240
## 2667 0 27.31751 41.11298 33.51768
## 2669 0 27.61339 40.82644 33.58309
## 2671 0 27.90661 40.54014 33.64863
## 2673 0 28.19609 40.27338 33.71430
## 2675 0 28.49678 40.06086 33.78009
## 2677 0 28.78249 39.84688 33.84601
## 2679 0 29.06993 39.63330 33.91206
## 2681 0 29.34846 39.42863 33.97824
## 2683 0 29.60349 39.19437 34.04455
## 2685 0 29.87907 38.97263 34.11099
## 2687 0 30.13658 38.77901 34.17755
## 2689 0 30.37774 38.59949 34.24425
## 2691 0 30.60230 38.46750 34.31108
## 2693 0 30.83041 38.29356 34.37804
## 2695 0 31.02157 38.23188 34.44513
## 2697 0 31.18995 38.15239 34.51235
## 2699 0 31.33233 38.14010 34.57970
## 2701 0 31.45404 38.13786 34.64718
## 2703 0 31.54964 38.17331 34.71479
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## 18123 0 25.86701 33.17507 29.31779
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## 18423 0 25.23453 31.32419 28.15984
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## 18429 0 25.86701 33.17507 29.31779
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## 18439 0 26.70693 36.85686 31.35448
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## 18839 0 26.05854 33.84817 29.71426
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## 18847 0 26.70693 36.85686 31.35448
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## 18933 0 25.23453 31.32419 28.15984
## 18935 0 25.45943 31.92001 28.54065
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## 18939 0 25.86701 33.17507 29.31779
## 18941 0 26.05854 33.84817 29.71426
## 18943 0 26.21357 34.54431 30.11609
## 18945 0 26.37626 35.29025 30.52335
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## 18949 0 26.70693 36.85686 31.35448
## 18951 0 26.86474 37.65133 31.77849
## 18953 0 27.02690 38.47872 32.20824
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## 18981 0 15.58895 24.66369 19.59390
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## 18993 0 17.79463 25.38332 21.23845
## 18995 0 18.17912 25.49154 21.52566
## 18997 0 18.57215 25.61778 21.81676
## 18999 0 18.96540 25.76825 22.11179
## 19001 0 19.37702 25.91618 22.41081
## 19003 0 19.79601 26.07421 22.71388
## 19005 0 20.18748 26.26643 23.02104
## 19007 0 20.59081 26.42379 23.33236
## 19009 0 20.97506 26.62791 23.64789
## 19011 0 21.37696 26.83039 23.96768
## 19013 0 21.76946 27.02863 24.29180
## 19015 0 22.16818 27.27195 24.62030
## 19017 0 22.54659 27.53704 24.95325
## 19019 0 22.90489 27.85148 25.29069
## 19021 0 23.27839 28.17467 25.63270
## 19023 0 23.60414 28.51177 25.97934
## 19025 0 23.90932 28.89131 26.33066
## 19027 0 24.19195 29.34228 26.68674
## 19029 0 24.49094 29.76627 27.04762
## 19031 0 24.76850 30.25490 27.41339
## 19033 0 25.02124 30.78533 27.78411
## 19035 0 25.23453 31.32419 28.15984
## 19037 0 25.45943 31.92001 28.54065
## 19039 0 25.66199 32.53971 28.92661
## 19041 0 25.86701 33.17507 29.31779
## 19043 0 26.05854 33.84817 29.71426
## 19045 0 26.21357 34.54431 30.11609
## 19047 0 26.37626 35.29025 30.52335
## 19049 0 26.52741 36.03244 30.93613
## 19051 0 26.70693 36.85686 31.35448
## 19053 0 26.86474 37.65133 31.77849
## 19055 0 27.02690 38.47872 32.20824
## 19057 0 27.16594 39.34121 32.64380
## 19059 0 27.26715 40.21130 33.08524
## 19061 0 27.37779 41.11638 33.53266
## 19063 0 27.51333 42.03735 33.98613
## 19065 0 27.62984 42.99925 34.44573
## 19067 0 27.77906 44.01949 34.91155
## 19069 0 27.90893 45.02005 35.38366
## 19071 0 28.02474 45.99019 35.86216
## 19073 0 28.14383 47.03567 36.34713
## 19075 0 23.76988 28.69564 26.16290
## 19077 0 14.55759 24.33564 18.82001
## 19079 0 14.88455 24.45309 19.07451
## 19081 0 15.23381 24.55013 19.33246
## 19083 0 15.58895 24.66369 19.59390
## 19085 0 15.93776 24.75273 19.85887
## 19087 0 16.31375 24.87721 20.12742
## 19089 0 16.68098 24.99282 20.39961
## 19091 0 17.04404 25.13130 20.67548
## 19093 0 17.41657 25.25163 20.95507
## 19095 0 17.79463 25.38332 21.23845
## 19097 0 18.17912 25.49154 21.52566
## 19099 0 18.57215 25.61778 21.81676
## 19101 0 18.96540 25.76825 22.11179
## 19103 0 19.37702 25.91618 22.41081
## 19105 0 19.79601 26.07421 22.71388
## 19107 0 20.18748 26.26643 23.02104
## 19109 0 20.59081 26.42379 23.33236
## 19111 0 20.97506 26.62791 23.64789
## 19113 0 21.37696 26.83039 23.96768
## 19115 0 21.76946 27.02863 24.29180
## 19117 0 22.16818 27.27195 24.62030
## 19119 0 22.54659 27.53704 24.95325
## 19121 0 22.90489 27.85148 25.29069
## 19123 0 23.27839 28.17467 25.63270
## 19125 0 23.60414 28.51177 25.97934
## 19127 0 23.90932 28.89131 26.33066
## 19129 0 24.19195 29.34228 26.68674
## 19131 0 24.49094 29.76627 27.04762
## 19133 0 24.76850 30.25490 27.41339
## 19135 0 25.02124 30.78533 27.78411
## 19137 0 25.23453 31.32419 28.15984
## 19139 0 25.45943 31.92001 28.54065
## 19141 0 25.66199 32.53971 28.92661
## 19143 0 25.86701 33.17507 29.31779
## 19145 0 26.05854 33.84817 29.71426
## 19147 0 26.21357 34.54431 30.11609
## 19149 0 26.37626 35.29025 30.52335
## 19151 0 26.52741 36.03244 30.93613
## 19153 0 26.70693 36.85686 31.35448
## 19155 0 26.86474 37.65133 31.77849
## 19157 0 27.02690 38.47872 32.20824
## 19159 0 27.16594 39.34121 32.64380
## 19161 0 27.26715 40.21130 33.08524
## 19163 0 27.37779 41.11638 33.53266
## 19165 0 27.51333 42.03735 33.98613
## 19167 0 27.62984 42.99925 34.44573
## 19169 0 27.77906 44.01949 34.91155
## 19171 0 27.90893 45.02005 35.38366
## 19173 0 28.02474 45.99019 35.86216
## 19175 0 28.14383 47.03567 36.34713
## 19177 0 23.76988 28.69564 26.16290
## 19179 0 14.55759 24.33564 18.82001
## 19181 0 14.88455 24.45309 19.07451
## 19183 0 15.23381 24.55013 19.33246
## 19185 0 15.58895 24.66369 19.59390
## 19187 0 15.93776 24.75273 19.85887
## 19189 0 16.31375 24.87721 20.12742
## 19191 0 16.68098 24.99282 20.39961
## 19193 0 17.04404 25.13130 20.67548
## 19195 0 17.41657 25.25163 20.95507
## 19197 0 17.79463 25.38332 21.23845
## 19199 0 18.17912 25.49154 21.52566
## 19201 0 18.57215 25.61778 21.81676
## 19203 0 18.96540 25.76825 22.11179
## 19205 0 19.37702 25.91618 22.41081
## 19207 0 19.79601 26.07421 22.71388
## 19209 0 20.18748 26.26643 23.02104
## 19211 0 20.59081 26.42379 23.33236
## 19213 0 20.97506 26.62791 23.64789
## 19215 0 21.37696 26.83039 23.96768
## 19217 0 21.76946 27.02863 24.29180
## 19219 0 22.16818 27.27195 24.62030
## 19221 0 22.54659 27.53704 24.95325
## 19223 0 22.90489 27.85148 25.29069
## 19225 0 23.27839 28.17467 25.63270
## 19227 0 23.60414 28.51177 25.97934
## 19229 0 23.90932 28.89131 26.33066
## 19231 0 24.19195 29.34228 26.68674
## 19233 0 24.49094 29.76627 27.04762
## 19235 0 24.76850 30.25490 27.41339
## 19237 0 25.02124 30.78533 27.78411
## 19239 0 25.23453 31.32419 28.15984
## 19241 0 25.45943 31.92001 28.54065
## 19243 0 25.66199 32.53971 28.92661
## 19245 0 25.86701 33.17507 29.31779
## 19247 0 26.05854 33.84817 29.71426
## 19249 0 26.21357 34.54431 30.11609
## 19251 0 26.37626 35.29025 30.52335
## 19253 0 26.52741 36.03244 30.93613
## 19255 0 26.70693 36.85686 31.35448
## 19257 0 26.86474 37.65133 31.77849
## 19259 0 27.02690 38.47872 32.20824
## 19261 0 27.16594 39.34121 32.64380
## 19263 0 27.26715 40.21130 33.08524
## 19265 0 27.37779 41.11638 33.53266
## 19267 0 27.51333 42.03735 33.98613
## 19269 0 27.62984 42.99925 34.44573
## 19271 0 27.77906 44.01949 34.91155
## 19273 0 27.90893 45.02005 35.38366
## 19275 0 28.02474 45.99019 35.86216
## 19277 0 28.14383 47.03567 36.34713
## 19279 0 23.76988 28.69564 26.16290
## 19281 0 14.55759 24.33564 18.82001
## 19283 0 14.88455 24.45309 19.07451
## 19285 0 15.23381 24.55013 19.33246
## 19287 0 15.58895 24.66369 19.59390
## 19289 0 15.93776 24.75273 19.85887
## 19291 0 16.31375 24.87721 20.12742
## 19293 0 16.68098 24.99282 20.39961
## 19295 0 17.04404 25.13130 20.67548
## 19297 0 17.41657 25.25163 20.95507
## 19299 0 17.79463 25.38332 21.23845
## 19301 0 18.17912 25.49154 21.52566
## 19303 0 18.57215 25.61778 21.81676
## 19305 0 18.96540 25.76825 22.11179
## 19307 0 19.37702 25.91618 22.41081
## 19309 0 19.79601 26.07421 22.71388
## 19311 0 20.18748 26.26643 23.02104
## 19313 0 20.59081 26.42379 23.33236
## 19315 0 20.97506 26.62791 23.64789
## 19317 0 21.37696 26.83039 23.96768
## 19319 0 21.76946 27.02863 24.29180
## 19321 0 22.16818 27.27195 24.62030
## 19323 0 22.54659 27.53704 24.95325
## 19325 0 22.90489 27.85148 25.29069
## 19327 0 23.27839 28.17467 25.63270
## 19329 0 23.60414 28.51177 25.97934
## 19331 0 23.90932 28.89131 26.33066
## 19333 0 24.19195 29.34228 26.68674
## 19335 0 24.49094 29.76627 27.04762
## 19337 0 24.76850 30.25490 27.41339
## 19339 0 25.02124 30.78533 27.78411
## 19341 0 25.23453 31.32419 28.15984
## 19343 0 25.45943 31.92001 28.54065
## 19345 0 25.66199 32.53971 28.92661
## 19347 0 25.86701 33.17507 29.31779
## 19349 0 26.05854 33.84817 29.71426
## 19351 0 26.21357 34.54431 30.11609
## 19353 0 26.37626 35.29025 30.52335
## 19355 0 26.52741 36.03244 30.93613
## 19357 0 26.70693 36.85686 31.35448
## 19359 0 26.86474 37.65133 31.77849
## 19361 0 27.02690 38.47872 32.20824
## 19363 0 27.16594 39.34121 32.64380
## 19365 0 27.26715 40.21130 33.08524
## 19367 0 27.37779 41.11638 33.53266
## 19369 0 27.51333 42.03735 33.98613
## 19371 0 27.62984 42.99925 34.44573
## 19373 0 27.77906 44.01949 34.91155
## 19375 0 27.90893 45.02005 35.38366
## 19377 0 28.02474 45.99019 35.86216
## 19379 0 28.14383 47.03567 36.34713
## 19381 0 23.76988 28.69564 26.16290
## 19383 0 14.55759 24.33564 18.82001
## 19385 0 14.88455 24.45309 19.07451
## 19387 0 15.23381 24.55013 19.33246
## 19389 0 15.58895 24.66369 19.59390
## 19391 0 15.93776 24.75273 19.85887
## 19393 0 16.31375 24.87721 20.12742
## 19395 0 16.68098 24.99282 20.39961
## 19397 0 17.04404 25.13130 20.67548
## 19399 0 17.41657 25.25163 20.95507
## 19401 0 17.79463 25.38332 21.23845
## 19403 0 18.17912 25.49154 21.52566
## 19405 0 18.57215 25.61778 21.81676
## 19407 0 18.96540 25.76825 22.11179
## 19409 0 19.37702 25.91618 22.41081
## 19411 0 19.79601 26.07421 22.71388
## 19413 0 20.18748 26.26643 23.02104
## 19415 0 20.59081 26.42379 23.33236
## 19417 0 20.97506 26.62791 23.64789
## 19419 0 21.37696 26.83039 23.96768
## 19421 0 21.76946 27.02863 24.29180
## 19423 0 22.16818 27.27195 24.62030
## 19425 0 22.54659 27.53704 24.95325
## 19427 0 22.90489 27.85148 25.29069
## 19429 0 23.27839 28.17467 25.63270
## 19431 0 23.60414 28.51177 25.97934
## 19433 0 23.90932 28.89131 26.33066
## 19435 0 24.19195 29.34228 26.68674
## 19437 0 24.49094 29.76627 27.04762
## 19439 0 24.76850 30.25490 27.41339
## 19441 0 25.02124 30.78533 27.78411
## 19443 0 25.23453 31.32419 28.15984
## 19445 0 25.45943 31.92001 28.54065
## 19447 0 25.66199 32.53971 28.92661
## 19449 0 25.86701 33.17507 29.31779
## 19451 0 26.05854 33.84817 29.71426
## 19453 0 26.21357 34.54431 30.11609
## 19455 0 26.37626 35.29025 30.52335
## 19457 0 26.52741 36.03244 30.93613
## 19459 0 26.70693 36.85686 31.35448
## 19461 0 26.86474 37.65133 31.77849
## 19463 0 27.02690 38.47872 32.20824
## 19465 0 27.16594 39.34121 32.64380
## 19467 0 27.26715 40.21130 33.08524
## 19469 0 27.37779 41.11638 33.53266
## 19471 0 27.51333 42.03735 33.98613
## 19473 0 27.62984 42.99925 34.44573
## 19475 0 27.77906 44.01949 34.91155
## 19477 0 27.90893 45.02005 35.38366
## 19479 0 28.02474 45.99019 35.86216
## 19481 0 28.14383 47.03567 36.34713
## 19483 0 23.76988 28.69564 26.16290
## 19485 0 14.55759 24.33564 18.82001
## 19487 0 14.88455 24.45309 19.07451
## 19489 0 15.23381 24.55013 19.33246
## 19491 0 15.58895 24.66369 19.59390
## 19493 0 15.93776 24.75273 19.85887
## 19495 0 16.31375 24.87721 20.12742
## 19497 0 16.68098 24.99282 20.39961
## 19499 0 17.04404 25.13130 20.67548
## 19501 0 17.41657 25.25163 20.95507
## 19503 0 17.79463 25.38332 21.23845
## 19505 0 18.17912 25.49154 21.52566
## 19507 0 18.57215 25.61778 21.81676
## 19509 0 18.96540 25.76825 22.11179
## 19511 0 19.37702 25.91618 22.41081
## 19513 0 19.79601 26.07421 22.71388
## 19515 0 20.18748 26.26643 23.02104
## 19517 0 20.59081 26.42379 23.33236
## 19519 0 20.97506 26.62791 23.64789
## 19521 0 21.37696 26.83039 23.96768
## 19523 0 21.76946 27.02863 24.29180
## 19525 0 22.16818 27.27195 24.62030
## 19527 0 22.54659 27.53704 24.95325
## 19529 0 22.90489 27.85148 25.29069
## 19531 0 23.27839 28.17467 25.63270
## 19533 0 23.60414 28.51177 25.97934
## 19535 0 23.90932 28.89131 26.33066
## 19537 0 24.19195 29.34228 26.68674
## 19539 0 24.49094 29.76627 27.04762
## 19541 0 24.76850 30.25490 27.41339
## 19543 0 25.02124 30.78533 27.78411
## 19545 0 25.23453 31.32419 28.15984
## 19547 0 25.45943 31.92001 28.54065
## 19549 0 25.66199 32.53971 28.92661
## 19551 0 25.86701 33.17507 29.31779
## 19553 0 26.05854 33.84817 29.71426
## 19555 0 26.21357 34.54431 30.11609
## 19557 0 26.37626 35.29025 30.52335
## 19559 0 26.52741 36.03244 30.93613
## 19561 0 26.70693 36.85686 31.35448
## 19563 0 26.86474 37.65133 31.77849
## 19565 0 27.02690 38.47872 32.20824
## 19567 0 27.16594 39.34121 32.64380
## 19569 0 27.26715 40.21130 33.08524
## 19571 0 27.37779 41.11638 33.53266
## 19573 0 27.51333 42.03735 33.98613
## 19575 0 27.62984 42.99925 34.44573
## 19577 0 27.77906 44.01949 34.91155
## 19579 0 27.90893 45.02005 35.38366
## 19581 0 28.02474 45.99019 35.86216
## 19583 0 28.14383 47.03567 36.34713
## 19585 0 23.76988 28.69564 26.16290
## 19587 0 14.55759 24.33564 18.82001
## 19589 0 14.88455 24.45309 19.07451
## 19591 0 15.23381 24.55013 19.33246
## 19593 0 15.58895 24.66369 19.59390
## 19595 0 15.93776 24.75273 19.85887
## 19597 0 16.31375 24.87721 20.12742
## 19599 0 16.68098 24.99282 20.39961
## 19601 0 17.04404 25.13130 20.67548
## 19603 0 17.41657 25.25163 20.95507
## 19605 0 17.79463 25.38332 21.23845
## 19607 0 18.17912 25.49154 21.52566
## 19609 0 18.57215 25.61778 21.81676
## 19611 0 18.96540 25.76825 22.11179
## 19613 0 19.37702 25.91618 22.41081
## 19615 0 19.79601 26.07421 22.71388
## 19617 0 20.18748 26.26643 23.02104
## 19619 0 20.59081 26.42379 23.33236
## 19621 0 20.97506 26.62791 23.64789
## 19623 0 21.37696 26.83039 23.96768
## 19625 0 21.76946 27.02863 24.29180
## 19627 0 22.16818 27.27195 24.62030
## 19629 0 22.54659 27.53704 24.95325
## 19631 0 22.90489 27.85148 25.29069
## 19633 0 23.27839 28.17467 25.63270
## 19635 0 23.60414 28.51177 25.97934
## 19637 0 23.90932 28.89131 26.33066
## 19639 0 24.19195 29.34228 26.68674
## 19641 0 24.49094 29.76627 27.04762
## 19643 0 24.76850 30.25490 27.41339
## 19645 0 25.02124 30.78533 27.78411
## 19647 0 25.23453 31.32419 28.15984
## 19649 0 25.45943 31.92001 28.54065
## 19651 0 25.66199 32.53971 28.92661
## 19653 0 25.86701 33.17507 29.31779
## 19655 0 26.05854 33.84817 29.71426
## 19657 0 26.21357 34.54431 30.11609
## 19659 0 26.37626 35.29025 30.52335
## 19661 0 26.52741 36.03244 30.93613
## 19663 0 26.70693 36.85686 31.35448
## 19665 0 26.86474 37.65133 31.77849
## 19667 0 27.02690 38.47872 32.20824
## 19669 0 27.16594 39.34121 32.64380
## 19671 0 27.26715 40.21130 33.08524
## 19673 0 27.37779 41.11638 33.53266
## 19675 0 27.51333 42.03735 33.98613
## 19677 0 27.62984 42.99925 34.44573
## 19679 0 27.77906 44.01949 34.91155
## 19681 0 27.90893 45.02005 35.38366
## 19683 0 28.02474 45.99019 35.86216
## 19685 0 28.14383 47.03567 36.34713
## 19687 0 23.76988 28.69564 26.16290
## 19689 0 14.55759 24.33564 18.82001
## 19691 0 14.88455 24.45309 19.07451
## 19693 0 15.23381 24.55013 19.33246
## 19695 0 15.58895 24.66369 19.59390
## 19697 0 15.93776 24.75273 19.85887
## 19699 0 16.31375 24.87721 20.12742
## 19701 0 16.68098 24.99282 20.39961
## 19703 0 17.04404 25.13130 20.67548
## 19705 0 17.41657 25.25163 20.95507
## 19707 0 17.79463 25.38332 21.23845
## 19709 0 18.17912 25.49154 21.52566
## 19711 0 18.57215 25.61778 21.81676
## 19713 0 18.96540 25.76825 22.11179
## 19715 0 19.37702 25.91618 22.41081
## 19717 0 19.79601 26.07421 22.71388
## 19719 0 20.18748 26.26643 23.02104
## 19721 0 20.59081 26.42379 23.33236
## 19723 0 20.97506 26.62791 23.64789
## 19725 0 21.37696 26.83039 23.96768
## 19727 0 21.76946 27.02863 24.29180
## 19729 0 22.16818 27.27195 24.62030
## 19731 0 22.54659 27.53704 24.95325
## 19733 0 22.90489 27.85148 25.29069
## 19735 0 23.27839 28.17467 25.63270
## 19737 0 23.60414 28.51177 25.97934
## 19739 0 23.90932 28.89131 26.33066
## 19741 0 24.19195 29.34228 26.68674
## 19743 0 24.49094 29.76627 27.04762
## 19745 0 24.76850 30.25490 27.41339
## 19747 0 25.02124 30.78533 27.78411
## 19749 0 25.23453 31.32419 28.15984
## 19751 0 25.45943 31.92001 28.54065
## 19753 0 25.66199 32.53971 28.92661
## 19755 0 25.86701 33.17507 29.31779
## 19757 0 26.05854 33.84817 29.71426
## 19759 0 26.21357 34.54431 30.11609
## 19761 0 26.37626 35.29025 30.52335
## 19763 0 26.52741 36.03244 30.93613
## 19765 0 26.70693 36.85686 31.35448
## 19767 0 26.86474 37.65133 31.77849
## 19769 0 27.02690 38.47872 32.20824
## 19771 0 27.16594 39.34121 32.64380
## 19773 0 27.26715 40.21130 33.08524
## 19775 0 27.37779 41.11638 33.53266
## 19777 0 27.51333 42.03735 33.98613
## 19779 0 27.62984 42.99925 34.44573
## 19781 0 27.77906 44.01949 34.91155
## 19783 0 27.90893 45.02005 35.38366
## 19785 0 28.02474 45.99019 35.86216
## 19787 0 28.14383 47.03567 36.34713
## 19789 0 23.76988 28.69564 26.16290
## 19791 0 14.55759 24.33564 18.82001
## 19793 0 14.88455 24.45309 19.07451
## 19795 0 15.23381 24.55013 19.33246
## 19797 0 15.58895 24.66369 19.59390
## 19799 0 15.93776 24.75273 19.85887
## 19801 0 16.31375 24.87721 20.12742
## 19803 0 16.68098 24.99282 20.39961
## 19805 0 17.04404 25.13130 20.67548
## 19807 0 17.41657 25.25163 20.95507
## 19809 0 17.79463 25.38332 21.23845
## 19811 0 18.17912 25.49154 21.52566
## 19813 0 18.57215 25.61778 21.81676
## 19815 0 18.96540 25.76825 22.11179
## 19817 0 19.37702 25.91618 22.41081
## 19819 0 19.79601 26.07421 22.71388
## 19821 0 20.18748 26.26643 23.02104
## 19823 0 20.59081 26.42379 23.33236
## 19825 0 20.97506 26.62791 23.64789
## 19827 0 21.37696 26.83039 23.96768
## 19829 0 21.76946 27.02863 24.29180
## 19831 0 22.16818 27.27195 24.62030
## 19833 0 22.54659 27.53704 24.95325
## 19835 0 22.90489 27.85148 25.29069
## 19837 0 23.27839 28.17467 25.63270
## 19839 0 23.60414 28.51177 25.97934
## 19841 0 23.90932 28.89131 26.33066
## 19843 0 24.19195 29.34228 26.68674
## 19845 0 24.49094 29.76627 27.04762
## 19847 0 24.76850 30.25490 27.41339
## 19849 0 25.02124 30.78533 27.78411
## 19851 0 25.23453 31.32419 28.15984
## 19853 0 25.45943 31.92001 28.54065
## 19855 0 25.66199 32.53971 28.92661
## 19857 0 25.86701 33.17507 29.31779
## 19859 0 26.05854 33.84817 29.71426
## 19861 0 26.21357 34.54431 30.11609
## 19863 0 26.37626 35.29025 30.52335
## 19865 0 26.52741 36.03244 30.93613
## 19867 0 26.70693 36.85686 31.35448
## 19869 0 26.86474 37.65133 31.77849
## 19871 0 27.02690 38.47872 32.20824
## 19873 0 27.16594 39.34121 32.64380
## 19875 0 27.26715 40.21130 33.08524
## 19877 0 27.37779 41.11638 33.53266
## 19879 0 27.51333 42.03735 33.98613
## 19881 0 27.62984 42.99925 34.44573
## 19883 0 27.77906 44.01949 34.91155
## 19885 0 27.90893 45.02005 35.38366
## 19887 0 28.02474 45.99019 35.86216
## 19889 0 28.14383 47.03567 36.34713
## 19891 0 23.76988 28.69564 26.16290
## 19893 0 14.55759 24.33564 18.82001
## 19895 0 14.88455 24.45309 19.07451
## 19897 0 15.23381 24.55013 19.33246
## 19899 0 15.58895 24.66369 19.59390
## 19901 0 15.93776 24.75273 19.85887
## 19903 0 16.31375 24.87721 20.12742
## 19905 0 16.68098 24.99282 20.39961
## 19907 0 17.04404 25.13130 20.67548
## 19909 0 17.41657 25.25163 20.95507
## 19911 0 17.79463 25.38332 21.23845
## 19913 0 18.17912 25.49154 21.52566
## 19915 0 18.57215 25.61778 21.81676
## 19917 0 18.96540 25.76825 22.11179
## 19919 0 19.37702 25.91618 22.41081
## 19921 0 19.79601 26.07421 22.71388
## 19923 0 20.18748 26.26643 23.02104
## 19925 0 20.59081 26.42379 23.33236
## 19927 0 20.97506 26.62791 23.64789
## 19929 0 21.37696 26.83039 23.96768
## 19931 0 21.76946 27.02863 24.29180
## 19933 0 22.16818 27.27195 24.62030
## 19935 0 22.54659 27.53704 24.95325
## 19937 0 22.90489 27.85148 25.29069
## 19939 0 23.27839 28.17467 25.63270
## 19941 0 23.60414 28.51177 25.97934
## 19943 0 23.90932 28.89131 26.33066
## 19945 0 24.19195 29.34228 26.68674
## 19947 0 24.49094 29.76627 27.04762
## 19949 0 24.76850 30.25490 27.41339
## 19951 0 25.02124 30.78533 27.78411
## 19953 0 25.23453 31.32419 28.15984
## 19955 0 25.45943 31.92001 28.54065
## 19957 0 25.66199 32.53971 28.92661
## 19959 0 25.86701 33.17507 29.31779
## 19961 0 26.05854 33.84817 29.71426
## 19963 0 26.21357 34.54431 30.11609
## 19965 0 26.37626 35.29025 30.52335
## 19967 0 26.52741 36.03244 30.93613
## 19969 0 26.70693 36.85686 31.35448
## 19971 0 26.86474 37.65133 31.77849
## 19973 0 27.02690 38.47872 32.20824
## 19975 0 27.16594 39.34121 32.64380
## 19977 0 27.26715 40.21130 33.08524
## 19979 0 27.37779 41.11638 33.53266
## 19981 0 27.51333 42.03735 33.98613
## 19983 0 27.62984 42.99925 34.44573
## 19985 0 27.77906 44.01949 34.91155
## 19987 0 27.90893 45.02005 35.38366
## 19989 0 28.02474 45.99019 35.86216
## 19991 0 28.14383 47.03567 36.34713
## 19993 0 23.76988 28.69564 26.16290
## 19995 0 14.55759 24.33564 18.82001
## 19997 0 14.88455 24.45309 19.07451
## 19999 0 15.23381 24.55013 19.33246
## 20001 0 15.58895 24.66369 19.59390
## 20003 0 15.93776 24.75273 19.85887
## 20005 0 16.31375 24.87721 20.12742
## 20007 0 16.68098 24.99282 20.39961
## 20009 0 17.04404 25.13130 20.67548
## 20011 0 17.41657 25.25163 20.95507
## 20013 0 17.79463 25.38332 21.23845
## 20015 0 18.17912 25.49154 21.52566
## 20017 0 18.57215 25.61778 21.81676
## 20019 0 18.96540 25.76825 22.11179
## 20021 0 19.37702 25.91618 22.41081
## 20023 0 19.79601 26.07421 22.71388
## 20025 0 20.18748 26.26643 23.02104
## 20027 0 20.59081 26.42379 23.33236
## 20029 0 20.97506 26.62791 23.64789
## 20031 0 21.37696 26.83039 23.96768
## 20033 0 21.76946 27.02863 24.29180
## 20035 0 22.16818 27.27195 24.62030
## 20037 0 22.54659 27.53704 24.95325
## 20039 0 22.90489 27.85148 25.29069
## 20041 0 23.27839 28.17467 25.63270
## 20043 0 23.60414 28.51177 25.97934
## 20045 0 23.90932 28.89131 26.33066
## 20047 0 24.19195 29.34228 26.68674
## 20049 0 24.49094 29.76627 27.04762
## 20051 0 24.76850 30.25490 27.41339
## 20053 0 25.02124 30.78533 27.78411
## 20055 0 25.23453 31.32419 28.15984
## 20057 0 25.45943 31.92001 28.54065
## 20059 0 25.66199 32.53971 28.92661
## 20061 0 25.86701 33.17507 29.31779
## 20063 0 26.05854 33.84817 29.71426
## 20065 0 26.21357 34.54431 30.11609
## 20067 0 26.37626 35.29025 30.52335
## 20069 0 26.52741 36.03244 30.93613
## 20071 0 26.70693 36.85686 31.35448
## 20073 0 26.86474 37.65133 31.77849
## 20075 0 27.02690 38.47872 32.20824
## 20077 0 27.16594 39.34121 32.64380
## 20079 0 27.26715 40.21130 33.08524
## 20081 0 27.37779 41.11638 33.53266
## 20083 0 27.51333 42.03735 33.98613
## 20085 0 27.62984 42.99925 34.44573
## 20087 0 27.77906 44.01949 34.91155
## 20089 0 27.90893 45.02005 35.38366
## 20091 0 28.02474 45.99019 35.86216
## 20093 0 28.14383 47.03567 36.34713
## 20095 0 23.76988 28.69564 26.16290
## 20097 0 14.55759 24.33564 18.82001
## 20099 0 14.88455 24.45309 19.07451
## 20101 0 15.23381 24.55013 19.33246
## 20103 0 15.58895 24.66369 19.59390
## 20105 0 15.93776 24.75273 19.85887
## 20107 0 16.31375 24.87721 20.12742
## 20109 0 16.68098 24.99282 20.39961
## 20111 0 17.04404 25.13130 20.67548
## 20113 0 17.41657 25.25163 20.95507
## 20115 0 17.79463 25.38332 21.23845
## 20117 0 18.17912 25.49154 21.52566
## 20119 0 18.57215 25.61778 21.81676
## 20121 0 18.96540 25.76825 22.11179
## 20123 0 19.37702 25.91618 22.41081
## 20125 0 19.79601 26.07421 22.71388
## 20127 0 20.18748 26.26643 23.02104
## 20129 0 20.59081 26.42379 23.33236
## 20131 0 20.97506 26.62791 23.64789
## 20133 0 21.37696 26.83039 23.96768
## 20135 0 21.76946 27.02863 24.29180
## 20137 0 22.16818 27.27195 24.62030
## 20139 0 22.54659 27.53704 24.95325
## 20141 0 22.90489 27.85148 25.29069
## 20143 0 23.27839 28.17467 25.63270
## 20145 0 23.60414 28.51177 25.97934
## 20147 0 23.90932 28.89131 26.33066
## 20149 0 24.19195 29.34228 26.68674
## 20151 0 24.49094 29.76627 27.04762
## 20153 0 24.76850 30.25490 27.41339
## 20155 0 25.02124 30.78533 27.78411
## 20157 0 25.23453 31.32419 28.15984
## 20159 0 25.45943 31.92001 28.54065
## 20161 0 25.66199 32.53971 28.92661
## 20163 0 25.86701 33.17507 29.31779
## 20165 0 26.05854 33.84817 29.71426
## 20167 0 26.21357 34.54431 30.11609
## 20169 0 26.37626 35.29025 30.52335
## 20171 0 26.52741 36.03244 30.93613
## 20173 0 26.70693 36.85686 31.35448
## 20175 0 26.86474 37.65133 31.77849
## 20177 0 27.02690 38.47872 32.20824
## 20179 0 27.16594 39.34121 32.64380
## 20181 0 27.26715 40.21130 33.08524
## 20183 0 27.37779 41.11638 33.53266
## 20185 0 27.51333 42.03735 33.98613
## 20187 0 27.62984 42.99925 34.44573
## 20189 0 27.77906 44.01949 34.91155
## 20191 0 27.90893 45.02005 35.38366
## 20193 0 28.02474 45.99019 35.86216
## 20195 0 28.14383 47.03567 36.34713
## 20197 0 23.76988 28.69564 26.16290
## 20199 0 14.55759 24.33564 18.82001
## 20201 0 14.88455 24.45309 19.07451
## [ reached getOption("max.print") -- omitted 201 rows ]### Plot amplitude lmer with trial number
pframe2$trt3 <- mapvalues(pframe2$trt2, from = c("Sham first", "Weighted first"),
to = c("Sham -> Weighted", "Weighted -> Sham"))
g0 <- ggplot(pframe2, aes(x=visitNum_centered, y=predMean))+
geom_line(aes(color = treatment))+
labs(y = expression ("Sonication amplitude "(m~s^{-2})), x = "Sonication number\n (0 is when treatment switched)") +
geom_ribbon(aes(x = visitNum_centered, ymin = blo, ymax = bhi, fill= treatment), alpha = 0.2) +
facet_wrap(~trt3) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
scale_fill_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = c(0.5, 0.89),
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0
ggsave(filename = file.path(figDir, "WeightedSham_Timeseries_amp.pdf"), width =5, height = 3.6)
g1 <- g0 + geom_point(data = newdf3[newdf3$visitNum_centered < 50,],
aes(x = visitNum_centered, y = amp_acc), position = position_jitter(width = 0.5), size = 0.1, pch = 16, alpha = 0.4) +
ylim(c(0, 165))
g1
ggsave(filename = file.path(figDir, "WeightedSham_Timeseries_withRawData.pdf"), width =5, height = 3.6)
g1 <- g0 + geom_point(data = newdf3[newdf3$visitNum_centered < 50,],
aes(x = visitNum_centered, y = amp_acc), position = position_jitter(width = 0.5), size = 0.1, pch = 16, alpha = 0.4) +
scale_y_log10(limits = c(2, 500)) +
annotation_logticks(sides = "l", color = 'grey', size = 0.2)
g1
ggsave(filename = file.path(figDir, "WeightedSham_Timeseries_withRawData_logScale.pdf"), width =5, height = 3.6)
# make figure that isn't faceted by order of treatment
g03 <- ggplot(pframe2, aes(x=visitNum_centered, y=predMean))+
geom_line(aes(color = treatment))+
labs(y = expression ("Sonication amplitude "(m~s^{-2})), x = "Sonication number\n (0 is when treatment switched)") +
geom_ribbon(aes(x = visitNum_centered, ymin = blo, ymax = bhi, fill= treatment), alpha = 0.2) +
facet_wrap(~treatment) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
scale_fill_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = c(0.75, 0.8),
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="vertical")
g03
ggsave(filename = file.path(figDir, "WeightedSham_Timeseries_trtFacet.pdf"), width =5, height = 3.6)Show amplitude plot without visit number
look at visit number 1 (right at the time of switching)
# mean and 95% CI (without visit number)
g0_amp <- ggplot(pframe2[pframe2$visitNum_centered %in% c(1) & pframe2$IT == ITmean, ], aes(x=treatment, y=predMean))+
geom_point(aes(color = treatment), alpha = 1) +
labs(y = expression ("Sonication amplitude "(m~s^{-2})), x = "Flower treatment") +
geom_errorbar(aes(x = treatment, ymin = blo, ymax = bhi, color= treatment), alpha = 1, width = 0.1) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, option = "A", begin =0, end = 0) +
theme(legend.position = "none",
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0_amp
ggsave(filename = file.path(figDir, "WeightedSham_Amp_pointWhiskers_BW.pdf"), width =2.5, height = 3)
g0 <- ggplot(pframe2[pframe2$visitNum_centered %in% c(1) & pframe2$IT == ITmean, ], aes(x=treatment, y=predMean))+
geom_point(aes(color = treatment), alpha = 1) +
labs(y = expression ("Sonication amplitude "(m~s^{-2})), x = "Flower treatment") +
geom_errorbar(aes(x = treatment, ymin = blo, ymax = bhi, color= treatment), alpha = 1, width = 0.1) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = "none",
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0
ggsave(filename = file.path(figDir, "WeightedSham_Amp_pointWhiskers.pdf"), width =5, height = 3.6)
# fig 2b
g0IT <- ggplot(pframe2[pframe2$visitNum_centered %in% c(1), ], aes(x=IT, y=predMean))+
geom_line(aes(color = treatment), alpha = 1) +
labs(y = expression ("Sonication amplitude "(m~s^{-2})), x = "Intertegular span (mm)") +
geom_ribbon(aes(x = IT, ymin = blo, ymax = bhi, fill = treatment), alpha = 0.2) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
scale_fill_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = "top",
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0IT
ggsave(g0IT, filename = file.path(figDir, "WeightedSham_Amp_IT_SUPP.pdf"), width =5, height = 3.6)
# make plot with rug
weight_rug <- g0IT + geom_rug(data = newdf3[!duplicated(newdf3$IT),], inherit.aes = FALSE, aes(x = IT))
weight_rug
ggsave(weight_rug, filename = file.path(figDir, "WeightedSham_Amp_IT_SUPP_rug.pdf"), width =5, height = 3.6)
Fig2b <- weight_rug
ITmean## [1] 3.965833g22 <- g0 +
annotate(geom="text", x=c(1,2), y=c(0, 0) + 40, label=c("a", "b"),
color="black")
ggsave(filename = file.path(figDir, "WeightedSham_Amp_pointWhiskers_annot.pdf"), width =5, height = 3.6)
## add raw data
g1 <- g0 + geom_point(data = newdf3, aes(x = treatment, y = amp_acc, color = treatment), position = position_jitter(width = 0.1, height = 6), alpha = 0.4, pch = 16, size = 0.2)
g1
ggsave(filename = file.path(figDir, "WeightedSham_amp_pointWhiskers_rawData.pdf"), width =5, height = 3.6)Put two plots into a single figure
major break – below this line is the first method I used
this is almost identical to the code above
Modeling frequency with lmer
Use BIC to select model (decide what interactions and covariates to use)
Make sure that REML = FALSE when comparing BIC values
Start with the biggest model of interest, and then see what predictors can be removed
# interaction that may be important, based on domain knowledge
m0 = lmer(freq ~ treatment*IT+ hive + (1|beeID), data = new_df, REML = FALSE)
# no interaction
m1 = lmer(freq ~ treatment+IT+ hive + (1|beeID), data = new_df, REML = FALSE)
BIC(m0, m1) # stay with m1 -- no interaction## df BIC
## m0 7 25187.77
## m1 6 25184.69anova(m0, m1) # this p-value is very borderline -- we're being ## Data: new_df
## Models:
## m1: freq ~ treatment + IT + hive + (1 | beeID)
## m0: freq ~ treatment * IT + hive + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m1 6 25150 25185 -12569 25138
## m0 7 25147 25188 -12567 25133 4.6848 1 0.03043 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# conservative to avoid overfitting by using BIC
m2 = lmer(freq ~ hive + IT+ (1|beeID), data = new_df, REML = FALSE)
BIC(m1, m2) # treatment doesn't make the model better## df BIC
## m1 6 25184.69
## m2 5 25178.53anova(m1, m2) # p-value for paper -- probably don't need to report## Data: new_df
## Models:
## m2: freq ~ hive + IT + (1 | beeID)
## m1: freq ~ treatment + IT + hive + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m2 5 25150 25178 -12570 25140
## m1 6 25150 25185 -12569 25138 1.6039 1 0.2054# p-value for hive
m3 = lmer(freq ~ treatment + (1|beeID), data = new_df, REML = FALSE)
anova(m1, m3)## Data: new_df
## Models:
## m3: freq ~ treatment + (1 | beeID)
## m1: freq ~ treatment + IT + hive + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m3 4 25146 25169 -12569 25138
## m1 6 25150 25185 -12569 25138 0.1592 2 0.9235# diagnostics -- use REML = TRUE
m1 <- update(m1, .~., REML =TRUE)
summary(m1) # summary for paper## Linear mixed model fit by REML ['lmerMod']
## Formula: freq ~ treatment + IT + hive + (1 | beeID)
## Data: new_df
##
## REML criterion at convergence: 25115.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3676 -0.4684 0.1873 0.6825 2.3319
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 954.3 30.89
## Residual 2357.8 48.56
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 355.173 61.937 5.734
## treatmentWeighted 2.614 2.065 1.266
## IT -1.833 15.543 -0.118
## hive4 -4.129 11.398 -0.362
##
## Correlation of Fixed Effects:
## (Intr) trtmnW IT
## trtmntWghtd -0.002
## IT -0.995 -0.016
## hive4 -0.047 0.000 -0.009plot(m1)
qqnorm(ranef(m1)$beeID[[1]])
qqline(ranef(m1)$beeID[[1]])
sjp.lmer(m1, type = "re", sort = TRUE) # plot random effects to find any outliers## Plotting random effects...
sjp.lmer(m1, type = 'fe', sort = TRUE, p.kr = FALSE) # plot fixed effects## Computing p-values via Wald-statistics approximation (treating t as Wald z).
Bootstrap CI’s for figure for paper
# set number of bootstrap replicates for models
nbootSims = 1000
table(new_df$hive) # more trials from hive 3##
## 3 4
## 1644 716# using hive 3, since it's the one with the most data
# however, hive doesn't affect model anyway
# calculate an average IT for prediction
ITmean = mean(tapply(new_df$IT, INDEX = new_df$beeID, FUN = function(x) x[1] ))
pframe <- data.frame(treatment = levels(droplevels(new_df$treatment)),
IT = ITmean,
hive = factor(3, levels = levels(new_df$hive)),
beeID = 99999)
pframe$freq <- 0
pp <- predict(m1, newdata = pframe, re.form=NA, type = 'response') # re.form sets all random effects to 0
### Calculate CI's (using bootstrap, not accounting for random effects)
bb2 <- bootMer(m1, FUN=function(x) predict(x, pframe, re.form=NA, type = 'response'), nsim = nbootSims)
print(paste("Number of bootstrap samples", nrow(bb2$t)))## [1] "Number of bootstrap samples 1000"bb2_se <-apply(bb2$t,2,function(x) quantile(x, probs = c(0.025, 0.975)))
pframe$blo<-bb2_se[1,]
pframe$bhi<-bb2_se[2,]
pframe$predMean <- pp
pframe <- pframe[, c('treatment', "blo", "bhi", "predMean")]
pframe## treatment blo bhi predMean
## 1 Sham 335.3492 359.8953 347.9021
## 2 Weighted 337.7346 363.1810 350.5156Make frequency plots for paper
# "Mean and bootstrap CI based on fixed-effects uncertainty ONLY"
g0 <- ggplot(pframe, aes(x=treatment, y=predMean))+
geom_point()+
labs(y = "Sonication frequency (Hz)", x = "Flower treatment") +
geom_errorbar(aes(ymin = blo, ymax = bhi), width = 0.1)
g0
ggsave(plot = g0, filename = file.path(figDir, "HeavyLight_PredsAndCI_freq.pdf"), width =4, height = 3)Modeling amplitude with lmer
# log transform for acceleration helps model fit better
# start with large model (including interaction)
ma0 = lmer(log(amp_acc) ~ treatment * IT + hive + (1|beeID), data = new_df, REML = FALSE)
ma1 = lmer(log(amp_acc) ~ treatment + IT + hive + (1|beeID), data = new_df, REML = FALSE)
BIC(ma0, ma1) # interaction, ma0, is better## df BIC
## ma0 7 4583.334
## ma1 6 4595.150# pval for interaction (in case paper needs it)
anova(ma0, ma1)## Data: new_df
## Models:
## ma1: log(amp_acc) ~ treatment + IT + hive + (1 | beeID)
## ma0: log(amp_acc) ~ treatment * IT + hive + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma1 6 4560.6 4595.1 -2274.3 4548.6
## ma0 7 4543.0 4583.3 -2264.5 4529.0 19.582 1 9.639e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ma2 <- update(ma0, .~. - hive)
BIC(ma0, ma2) # hive not important## df BIC
## ma0 7 4583.334
## ma2 6 4576.547#pval for hive
anova(ma0, ma2)## Data: new_df
## Models:
## ma2: log(amp_acc) ~ treatment + IT + (1 | beeID) + treatment:IT
## ma0: log(amp_acc) ~ treatment * IT + hive + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma2 6 4541.9 4576.5 -2265.0 4529.9
## ma0 7 4543.0 4583.3 -2264.5 4529.0 0.979 1 0.3224# fit with reml = TRUE for summarizing
ma3 <- update(ma2,.~., REML = TRUE)
summary(ma3) # final model to report## Linear mixed model fit by REML ['lmerMod']
## Formula: log(amp_acc) ~ treatment + IT + (1 | beeID) + treatment:IT
## Data: new_df
##
## REML criterion at convergence: 4545.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0179 -0.5395 0.1071 0.6826 2.6697
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07463 0.2732
## Residual 0.38434 0.6200
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.32401 0.58488 5.683
## treatmentWeighted -1.60422 0.30031 -5.342
## IT 0.05653 0.14700 0.385
## treatmentWeighted:IT 0.33294 0.07515 4.430
##
## Correlation of Fixed Effects:
## (Intr) trtmnW IT
## trtmntWghtd -0.301
## IT -0.996 0.300
## trtmntWg:IT 0.302 -0.996 -0.303# diagnostics
plot(ma3)
qqnorm(ranef(ma3)$beeID[[1]])
qqline(ranef(ma3)$beeID[[1]])
sjp.lmer(ma3) # plot random effects to find any outliers## Plotting random effects...
sjp.lmer(ma3, type = 'fe', sort = TRUE, p.kr = FALSE) # plot fixed effects## `sjp.lmer()` will become deprecated in the future. Please use `plot_model()` instead.## Computing p-values via Wald-statistics approximation (treating t as Wald z).
Bootstrap CI’s for amplitude for figure for paper
# set number of bootstrap replicates for models
nbootSims2 = 1000
# using hive 3, since it's the one with the most data
pframe <- data.frame(treatment = levels(droplevels(new_df$treatment)), IT = ITmean, hive = factor(3, levels = levels(new_df$hive)), beeID = 99999)
pframe$amp_acc <- 0
# exponentiate to put on original scale
pp <- exp(predict(ma3, newdata = pframe, re.form=NA, type = 'response')) # re.form sets all random effects to 0
### Calculate CI's (using bootstrap, not accounting for random effects)
bb2 <- bootMer(ma3, FUN=function(x) predict(x, pframe, re.form=NA, type = 'response'), nsim = nbootSims2)
print(paste("Number of bootstrap samples", nrow(bb2$t)))## [1] "Number of bootstrap samples 1000"bb2_se <-apply(bb2$t,2,function(x) quantile(x, probs = c(0.025, 0.975)))
pframe$blo<- exp(bb2_se[1,]) # exponentiate to put on original scale
pframe$bhi<- exp(bb2_se[2,])
pframe$predMean <- pp
pframe <- pframe[, c('treatment', "blo", "bhi", "predMean")]
pframe## treatment blo bhi predMean
## 1 Sham 31.55900 37.97060 34.75029
## 2 Weighted 23.82485 28.84456 26.16290Make amplitude plots for paper
# "Mean and bootstrap CI based on fixed-effects uncertainty ONLY"
# Holding IT = meanIT
print(ITmean)## [1] 3.965833ga0 <- ggplot(pframe, aes(x=treatment, y=predMean))+
geom_point()+
labs(y = expression ("Sonication amplitude "(m~s^{-2})), x = "Flower treatment") +
geom_errorbar(aes(ymin = blo, ymax = bhi), width = 0.1) +
annotate(geom="text", x=c(1,2), y=c(0, 0) + 40, label=c("a", "b"),
color="black")
ga0
ggsave(plot = ga0, filename = file.path(figDir, "HeavyLight_PredsAndCI_amp.pdf"), width =4, height = 3)Put two plots into a single figure
# refref: note I might want to align these two figure for paper (in one plot)
# WeightedSham_Amp_pointWhiskers_BW.pdf
# WeightedSham_Freq_pointWhiskers_BW.pdf
pfreq <- Fig2a
pamp <- Fig2b + theme(legend.position = c(.5,.85)) + ylim(c(10,55))
aa <- plot_grid(pfreq, pamp, align = 'h', axis = 'l', rel_widths = c(1,2))
ggdraw(aa)
ac <- plot_grid(pfreq, pamp, align = 'h', axis = 'l', rel_widths = c(1,2), labels = "AUTO")
ggdraw(ac)
save_plot(file.path(figDir, "CombinedFreqAmp_weightedSham4_noxlab_IT.pdf"), plot = aa, base_width = 7, base_height = 3)
save_plot(file.path(figDir, "CombinedFreqAmp_weightedSham4_annot_IT.pdf"), plot = ac, base_width = 7, base_height = 3)sessionInfo()## R version 3.4.2 (2017-09-28)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS High Sierra 10.13.2
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] cowplot_0.9.1 viridis_0.4.0 viridisLite_0.2.0
## [4] gamm4_0.2-5 mgcv_1.8-20 nlme_3.1-131
## [7] effects_4.0-0 carData_3.0-0 plyr_1.8.4
## [10] multcomp_1.4-8 TH.data_1.0-8 MASS_7.3-47
## [13] survival_2.41-3 mvtnorm_1.0-6 sjPlot_2.4.0
## [16] lme4_1.1-14 Matrix_1.2-11 reshape2_1.4.2
## [19] ggplot2_2.2.1
##
## loaded via a namespace (and not attached):
## [1] pbkrtest_0.4-7 RColorBrewer_1.1-2 rprojroot_1.2
## [4] tools_3.4.2 TMB_1.7.11 backports_1.1.1
## [7] R6_2.2.2 sjlabelled_1.0.5 DT_0.2
## [10] lazyeval_0.2.1 colorspace_1.3-2 nnet_7.3-12
## [13] gridExtra_2.3 tidyselect_0.2.3 mnormt_1.5-5
## [16] compiler_3.4.2 sandwich_2.4-0 labeling_0.3
## [19] scales_0.5.0 lmtest_0.9-35 psych_1.7.8
## [22] blme_1.0-4 stringr_1.2.0 digest_0.6.12
## [25] foreign_0.8-69 minqa_1.2.4 rmarkdown_1.8
## [28] stringdist_0.9.4.6 pkgconfig_2.0.1 htmltools_0.3.6
## [31] pwr_1.2-1 htmlwidgets_0.9 rlang_0.1.4
## [34] shiny_1.0.5 bindr_0.1 zoo_1.8-0
## [37] dplyr_0.7.4 magrittr_1.5 modeltools_0.2-21
## [40] bayesplot_1.4.0 Rcpp_0.12.13 munsell_0.4.3
## [43] abind_1.4-5 prediction_0.2.0 stringi_1.1.6
## [46] yaml_2.1.14 merTools_0.3.0 snakecase_0.5.1
## [49] grid_3.4.2 parallel_3.4.2 sjmisc_2.6.2
## [52] forcats_0.2.0 lattice_0.20-35 ggeffects_0.2.2
## [55] haven_1.1.0 splines_3.4.2 sjstats_0.12.0
## [58] knitr_1.17 codetools_0.2-15 stats4_3.4.2
## [61] glue_1.2.0 evaluate_0.10.1 modelr_0.1.1
## [64] nloptr_1.0.4 httpuv_1.3.5 gtable_0.2.0
## [67] purrr_0.2.4 tidyr_0.7.2 assertthat_0.2.0
## [70] mime_0.5 coin_1.2-1 xtable_1.8-2
## [73] broom_0.4.2 survey_3.32-1 coda_0.19-1
## [76] tibble_1.3.4 arm_1.9-3 glmmTMB_0.1.4
## [79] bindrcpp_0.2